While the number of such 熟語 out there is much less than 音・音 pairs and also 訓・訓 pairs, there are still plenty out there. Here's one I happily encountered the other day.

I moved appartment recently and was lucky enough to get all my 敷金（しき・きん） that I paid for on the first appartment back! Didn't think that happened in Japan.

Technically, I think しき is a nanori reading of 敷、but it's going in this thread anyway!

The Brain teaser thread was going slightly off topic hence the "need" for this thread.

Pretty sure しき is a 訓-reading here. Normally by itself 敷き would have き as okurigana, but often the okurigana is absorbed into kanji when they're in compounds (especially the first character in a compound) and that still doesn't make it nanori.

Another 訓・音 mixture with 敷 is 敷地, but 下敷き would usually include the okurigana.
Furikae is usually written 振替, not 振り替え.

JimmySeal and myself are both partial to some 無駄話 so I'll just carry on...

Personally, I class nanori readings as kunyomi. For me it keeps things simpler thinking in terms of 音 and 訓 only. But according to Jim Breen the above reading is a 'nanori'. It's listed as a "special reading" in my 常用漢字学習字典。

下敷き is such a great product. Wish I had one when I was at school!

無駄話 - nice ON-ON-KUN combo. 話 is another place where a verb tense has had its okurigana lopped off.

My take on 名乗り is that they're special readings for use in people's names (hence the word 名乗り), but I think in the case of 敷金 it's just a regular 連用形 with its okurigana missing and there's no need to bring nanori into this
I believe that okurigana usage used to be a bit looser in the past (Japanese originally had no okurigana at all), the seam waye speling in Inglish was less fixt in dayes gon bye (suche as in the tymes of Shakspear). I think this is just a carry-over from those olden days. Perhaps 食べ物 is a newer word, because it has to be written with okurigana, lest it become しょくもつ.

I once asked the Japanese teachers at my school a similar question about 音・訓・名乗り for the word 田舎. I found out a few interesting things. None of my teachers (国語 included) knew the word 名乗り to mean "name reading." They knew it as the other two edict meanings. I was then told that 田舎 was simply a "special reading" (I guess existing somewhere closer to 訓 than 音 but don't quote me on that) Then about 10 minutes later, I was handed a page from a 国語 text that had all of these words listed. I have no idea if it was complete and I have since lost the paper (thank god I typed it out).
The 熟字訓:
明日
小豆
海女
硫黄
意気地
一言居士
田舎
息吹
海原
乳母
浮気
浮つく
お父さん
叔父
伯父
お母さん
笑顔
大人
乙女
叔母
伯母
お巡りさん
お神酒
母屋
母家
神楽
河岸
風邪
仮名
蚊帳
為替
河原
川原
昨日
今日
果物
玄人
今朝
景色
心地
今年
早乙女
雑魚
桟敷
差し支える
五月晴れ
早苗
五月雨
時雨
竹刀
芝生
清水
三味線
砂利
数珠
上手
白髪
素人
師走
数奇屋
数寄屋
相撲
草履
山車
太刀
立ち退く
七夕
足袋
稚児
一日
築山
梅雨
凸凹
手伝う
伝馬船
投網
十重二十重
読経
時計
友達
仲人
名残
雪崩
兄さん
姉さん
野良
祝詞
博士
二十歳
二十
二十日
波止場
一人
日和
二人
二日
吹雪
下手
部屋
迷子
真っ赤
真っ青
土産
息子
眼鏡
猛者
紅葉
木綿
最寄り
八百長
八百屋
大和
浴衣
行方
寄席
若人

That's an amazing list! Thanks!

I've discussed the social aspect of nanori with a couple of my teachers. They say that more and more, parents just choose a name or kanji they fancy for their child and assign which ever kanji/reading suits them, even if it's not an ON/KUN reading for that kanji.

(These discussions came about because while the school has official lists for every student's kanji, there are no hiragana readings. I noticed how ridiculously inefficient it was for EVERY teacher to 1. have to ask EVERY student of EVERY class how to pronounce their names, then 2. make all their own name lists, seating charts, gradebooks, etc. (and 3. while I enjoy the practice, I was annoyed I had to do the same since it takes me so much longer).

In typical J fashion though, they responded that that's the way it's always been, so why change it? I offered the idea that upon registration, every student include furigana with their kanji. Then, when the office lady makes the official school name list spreadsheet, she include the hiragana also. Then, every teacher can simply cut and paste into whatever list they want. "Wow! That'd be so simple! That'd make it so much easier for all the teachers!," one teacher exclaimed. "But, sorry, it'll never change. It's too "difficult" to change," she added... )

Going off topic again but...

dingomick Wrote:In typical J fashion though, they responded that that's the way it's always been, so why change it? I offered the idea that upon registration, every student include furigana with their kanji. Then, when the office lady makes the official school name list spreadsheet, she include the hiragana also. Then, every teacher can simply cut and paste into whatever list they want. "Wow! That'd be so simple! That'd make it so much easier for all the teachers!," one teacher exclaimed. "But, sorry, it'll never change. It's too "difficult" to change," she added... )

Welcome to Japan! I just spent over an hour down the 郵便局 opening a savings account. At least I got time off work to head down there though.

my school has roll sheets with furigana for each kid's name. Guess I'm lucky ^_^

Though there are also roll sheets without the readings, so sometimes a teacher will mispronounce a name because of that. Also, the kids' name tags don't have the readings, so sometimes those cause problems.

I don't know the steps involved in enrolling a kid in school in Japan, but I can't imagine there is not a form at some step in the process with places to write both "name" and "furigana". Sounds like your school just has a super inefficient way of (not) getting that information to the teachers.

Off topic but related:

Welcome to Japan indeed! The banks and post offices are another excellent example of how inefficient Japan is because of custom. Can you imagine how many hundreds of millions of hours of lost productivity there are in Japan every year because of ridiculous operating hours for the bank (10-3?!?!) and post office ? It's just a matter of fact that every business/school/office must allow its employees to take time off of work to take care of these personal matters because of their operating hours.

On the other hand, banks in the US, as a matter of fact are, 1. open ~8-6 which allows some people to take care of business right before or after work and, 2. are usually open late one day of the week (till ~8) to allow day workers to take care of their business since they, of course, are not allowed to leave their job in the middle of the day to go to the bank.

And don't get me started on ATMs! They're machines! They don't need rest!

訓・音 combo list of words I come across as opposed to look for. Starts with...

手製　（て・せい） - handmade
敷金　（しき・きん） - deposit (when renting an appartment)

I've only just realised (found out) that 値段 is a 訓・音 combo...doh!