When 間【あいだ】に and うちに are preceded by nouns, are they always interchangeable? For example, in 春【はる】休【やす】みのあいだに/うちに友達【ともだち】と一緒【いっしょ】に出掛【でか】けたい。 And also in: 大学生【だいがくせい】のうちに/間【あいだ】に留学【りゅうがく】する。
Taken directly from the Dictionary of Japanese Grammar here at https://core6000.neocities.org/dojg/ :
"When it indicates an interval of time, aida refers to the 'time space' between two points, i.e., the beginning and the end. In other words, the time space indicated by aida can be measured in clocktime. Uchi, however, does not refer to such measurable time space; it simply means 'time space within'. Thus, in a situation where a mother wants to read books while her child is away at school, either uchi or aida can be used. However, in a situation where we want to play tennis before it rains, we cannot substitute aida for uchi, because it is impossible to specify a time boundary."
It then goes on to give the following example sentences (the asterisks mark what is incorrect):
(I read books while my child is away at school.)
(I'll go and play tennis before it rains.)
(Please drink the beer while it is cold.)
So the answer is no. They are not always interchangeable but in many cases they are.