Church teaching grants that adultery (and even more so, if repeatedly) constitute solid grounds for separation. You are not in obligation to continue living with that person.
Whoa, hold on there. Don't move out, or kick your husband out, based on this comment without more detail. It's not that simple!
1) Traditionally, the rare instance where a couple may separate is with the permission of a Bishop, which follows
2) intensive counsel to rehabilitate the marriage with a priest.
A Bishop approved separation happens under dire circuмstances such as violence, or scandal in front of the children. Marriage is too critical for the Church to permit this to happen commonly. Unfortunately, adultery is not uncommon for Catholics, so there would be a LOT of separations if that was the only criteria.
First - pray and fast. Constantly have the picture of Christ carrying the cross, it will strengthen you to carry yours, which is very heavy under these circuмstances. Also, find solace in the arms of Our Mother of Sorrows.
Second - see a priest. Take his counsel. "Do whatever he tells you."
Third - do not show anger or coldness toward your husband.
There is a great victory in being dignified. Don't ever give into the temptation of screaming and histrionics which is mostly an exhibition of self indulgence because we are hurt. Act like a grand dame at ALL TIMES, civilized, calm, composed. How would Mary behave? Then behave accordingly. Schedule your discussions so you have time to compose your thoughts and can express them quietly to him. You could even write your thoughts down to give to him. Catholics are dignified, and we bear our crosses with joy and acceptance. Always avoid the drama, which won't help a bit and will alienate him further, giving him justification in his current state of mind.
(quick note: medical test to ensure no communicable disease if there is a return to marital relations, but your priest will help you with this)
He must determine why he's a serial adulterer, sabotaging the holy sacrament of marriage and his family. You must help him to the best of your ability, which may be limited by his cooperation or other factors. In the end, your priest will guide you. Make sure he's traditional.