Is Ichabod Crane cheating on his wife?

Okey so, currently I'm watching the 3rd season of Sleepy Hollow and Ichabod Crane has all these flashbacks, right? I understand that currently his wife is dead, but back in the 18th century she was alive. So in his flashbacks he is still married. How come then that he is flirting (kissing) around with Betsy Ross? He seems too honourable for that.