Low fibre/low residue works best for me.
Peanut butter is one of the best foods I've found. It's cheap and easily available, high calorie, but the "good" kind of fats, and easy (for me) to digest (as long as it's smooth rather than crunchy).
Cooking things in olive oil also adds in some healthy fats.
I do well on supplements like Ensure. Especially when I just can't face eating much. I had previously been eating things that went down easily like ice cream when I couldn't stand sitting down to a whole cooked meal. My doctor recommended supplements as they're high calorie and have all the vitamins you need, so you don't need to worry about getting in all your vegetables - which are low calorie and usually difficult to digest as well.
I also agree with the post above that avocados are the best fruit to gain weight on, and east to digest.
If he is ok with dairy switching to full fat milk is an easy way to get more calories and you can add it into things like sauces. A low fibre breakfast cereal like Cornflakes or Rice Krispies is easy to digest, and by using full fat milk rather than semi/skimmed and adding sugar you can get in more calories without making it any more filling.
I also eat a lot of white bread products, such as plain scones with butter. White rather than brown or wholemeal is the easiest when you're flaring, and although opinions vary on whether butter is healthy - maybe olive oil based spreads are better? - it gets in a lot of calories and I find them very easy to eat.
I would say though that at really low weights calories can be more of a priority than making sure food is "healthy". With the weight loss your husband has experienced, he needs to eat whatever high calorie foods he can, and if what he really feels like eating happens to be unhealthy - e.g. chocolate - it's still going to do him more good than harm. It is so much easier to eat more when you're feeling bad if you allow yourself to eat what you fancy and enjoy - as long as it's not going to cause digestive problems. As long as he's getting all the right nutrients (supplements can help with this), calories should be the priority in the short term, and he can worry about not overdoing the bad fats when he's gained weight and is in a better position to do so.
Although the ideal would be that he can gain weight whilst still avoiding unhealthy fats, sugar, etc., but if he's finding it a struggle the unhealthy foods are not going to do him as much harm as being underweight. As well as feeling down and tired from weighing too little, if he's underweight and happens to get an acute phase of illness, he won't be able to recover as well as he would if he weighed more, and the longer he's underweight the greater the possibility that it will begin to affect things such as his bone density. So it isn't always the best thing to worry about the quality of the calories if it's hindering weight gain.
I'm also sorry your husband had to put up with suspicions that he's got HIV or is taking drugs. As a young, underweight female I get a lot of people - doctors especially - assuming I'm anorexic. It's really hard when you're incorrectly stereotyped. I imagine it's harder for an underweight man in this respect as the social pressure is to be muscular.
It's good to see how much you care about your husband, you are already doing him the best thing you can for his self esteem by showing him you care whatever he weighs and looks like.
