It is not possible. Without trust, it is merely a one-sided relationship.

So, he lies and he behaves inappropriately with other females when he is in a committed relationship with you, he keeps on behaving inappropriately over and over again, he disrespects you, he is untrustworthy.. yet he is a good husband?

The definition of a husband is someone who loves and respects their spouse and their words and actions are trustworthy. Your husband fails at all of these.