V.F.
My thought is a question for you. How do you (and your husband) respond when he answers truthfully - but something that is negative? If you get mad, then he has learned that telling the truth gets him in trouble.
That said, I don't think 3 year olds get the concept of lying. At this age it can also be a point of just saying things to see what you do. (My 2 year old ALWAYS answers 'no' - even when asked if he wants ice cream.)
I'd continue to talk to him, and see if you can tease the correct answer out of him. I jest with my kids and tease the answer out in a non-threatening manner. When given the accurate answer then I compliment them for telling me the truth. (Sometimes getting the truth is more important than getting the behavior corrected.) Positive reinforcement helps SO much.
Continue working with him on this. You are right about not wanting to deal with this long term. :)
Hope that is helpful.
-V