How can I trust him, if he is not honest?

Married less than a year. Hubby confided personal medical info about me to his ex girlfriend (both told me this). Calls her on regular basis after I expressed that I was not comfortable with the secret calls and meetings. He has never told me about her - what I know I have heard from others, we have not met and he does not know that the contact continues even after he said it had stopped.