If he has left the marital home where your child(ren) live with you for several days, weeks, months then this is called “abandonment” and it is a felony! You need to keep a journal and write down the date and time your husband left the home, dates and times he calls, dates and times he stops by, and if he interacts with your child, and keep this record confidential and hidden until you decide what to do. You may need to use this record in the future in case you go through a divorce, as it could greatly help your chances of gaining custody of your child! Just remember, DOCUMENT EVERYTHING! Here is a link to a website about laws and abandonment issues.
http://criminal.findlaw.com/criminal-charges/child-abandonment.html
I really hope all works out for you, and maybe this is a blessing in disguise for your future. I am sorry you are having to go thru this.
~Kaci