We rescued a male (approximately 2 years old) bichon in December. He was doing great and pooping and peeing outside without a problem. All of the sudden 2 weeks ago, he is marking the couch, chair and carpet in our great room. I use enzyme cleaner, have cleaned the carpets and couch, sprayed no more marking, and how have covered it all with sheets and sprayed no more marking on the sheets. We have never caught him in the act. He was never crated when we got him, and has had the run of the whole house.
Any suggestions on how we can stop this train wreck?

Has he been neutered. A lot of entire males will start marking at around this age :)

Yes, he has been neutered...

Hmm OK, next step...

Has anything changed?
Anything at all?
Some dogs begin marking because they feel insecure about their surroundings.

It's hard to stop him if you can't catch him in the act.
The enzyme cleaning is great.
Make yourself a shaker out of an empty bottle with some rocks in it and shake the bottle if you catch him then quickly take him outside.

You will need to keep a close eye on him so you can catch him which will be the hardest part...

Just found this site too which has some really good info on it :)

http://www.dogchatforum.com/dog-marking-inside.htm

Nothing has changed - we are both or one of us home most of the time. If we go out it is for less than 3 hours. He has a doggie door so he can go in and out any time. When he marks, it isn't very much... just the mark. The problem is that we have never caught him in the act. We were even in my office one day and he did it on my chair not ten feet away, but I was not paying attention to him so didn't see it. We're getting very frustrated!

Does he do it in certain areas all the time?
Or is it completely random?

One of my friends with shih tzus had to get doggy diapers because they just wouldn't stop marking.

He does it in one room only, and it is on one corner of the couch and one corner of a chair as well as the carpet around those areas. Times are completely random!

Try putting tin foil (yes it's going to look bad) on the areas he marks most... he will not only not like walking on it but when he pees it will make a noise and hopfully he will stop.
This may make him just move to another area though so it's up to you whether you think it's worth trying.