UNLESS is unusual in that type of condition. It is frequently presented as an alternative to IF...NOT, and some English course books and sites give exercises in which students must change one form into the other, with the (sometimes explicit) idea that there is no difference in meaning between such utterances as:
1. I'm going swimming tomorrow if it doesn't rain.
2, 'm going swimming tomorrow unless it rains.
In fact, as always in English, if a different word is used, there is some degree of difference in meaning, even if the practical difference is small. IF in #1 suggests uncertainty about the possibility of rain, and consequent uncertainty about the possibility of going swimming. UNLESS has a meaning similar to except in the following situation(s) or if and only if ... not; the certainty of going swimming is greater in the speaker's mind in #2 than in 1. How great or small the certainty is within the speaker's mind in each case is of course known only to the speaker at the time of utterance.
It is for this reason that in counterfactual hypotheses about the past, UNLESS is far less commonly used. In #3, below, the speaker mentions one situation that would have made his parents unhappy; the possibility exists of there being other situations that would equally have made them unhappy. #4 would imply that the parents would have been unhappy in every contingency except the speaker's going to university - theoretically possible but unlikely.
3. My parents would have been unhappy if I hadn't gone to university.
4. ?My parents would have been unhappy unless I had gone to university.
In addition, as we have discovered with #2 , the use of UNLESS implies that the certainty of the occurrence of the situation in the consequent clause is greater than with IF...NOT. The speaker is not likely to imply greater certainty of occurrence of something that he or she knows did not occur.