Well, you're right: Inherited property is considered separate (I'm in California, don't know where you are, so some things may or may not be different) but according the attorney I talked to after D-Day, there are some conditions to that rule. The first is that the inherited assets are given to YOU and only YOU. He said there's sometimes a loophole where the inheritance was given to one spouse with the intention of it being for both spouses use. Like, say, you get married and Granny Smith decides to cut you a check early for your part of the inheritance as a wedding gift. Then it's considered to be joint, because it was given with the intention of being used by both of you. If you two divorce, that money could be split as a result.
As for collecting rent on an inherited property, yes, get a separate account and put it in there. It's not so much that your H is entitled to it (I'm not an attorney, so I wouldn't want to give you legal advice in this matter), but that he may try to justify it as joint assets because you put the money in the joint account. If you're worried about this, play it safe. Definitely speak to an attorney to see what your options are, too.
I have a sizeable inheritance that has been coming to me in bits and pieces for the last 7 years or so. When D-Day happened, I wasn't thinking about protecting my assets, but everyone around me got very paranoid that H was going to try to get his hands on my inheritance if we divorced. H is a good soul and it didn't even cross his mind, but I got very paranoid as well and ended up discussing this with a lawyer to see what my options were if we split. In my situation, it's very cut and dried... We have separate bank accounts as it is, but even if I put the money in a joint account, it would still be considered separate property because it comes directly to me via my grandparents' estate.