Not sure why the down votes... You can be dishonest and truthful but you cannot be dishonest and honest. You can mix truths in with lies and that would still absolutely be considered dishonest, but you cannot mix lies into truths and still be honest.
You're assuming the answer must be binary, where "yes" means you're honest all the time and "no" means you're dishonest all the time. Those characters show up in riddles, but in reality, most people are somewhere on the scale in between perfectly-honest and perfectly-dishonest.
Even the question "are you an honest person?" would, to most people, mean "are you generally honest?" Either answer makes sense here.
The truely dishonest will happily use honesty when it's in their best interest, and the truely honest are aware that they have probably been dishonest at some point, and should say they try, but might have low self esteem and impossibly high self expectations leading them to say no, because they were dishonest that one time, and so know they're capable of it...
An actually honest answer would be something like "I try to be honest."
I would probably float something just like that. Add a bit of fake humility. Not too much.
If people are really looking for the truth, that will look like truth to them. It will also happen to be the truth, as vague as it is, so if they want to dig it won't be hard to carry on. Keep it reassuring. Don't actually say anything definite. Act pious. :]