Am i finish pushing him away,or what?

am i wronge for pushin my husband away,see the thing is he a cheater and a lier.eg..in the morning he greet me,and because am so upset i respond to him so selfishly,but i can help it.so i let him go to work without soeakin to him and am the same when he get back.am a very lovin person,outgoin and most of all intelligent and beautiful.i know he love comin home to me or wakin up on the side of me inspite of his ways.but i just cant accept that.not cause he greet me and say nice things.that doesnt mean i must still accept this from him.please help me.