First of all, there is the civil legal process of divorce, and then there is the sentiment that one is not married. According to the Church, these are two different things. This is because pretending that things are other than they are is not what is meant by being faithful in bad times. Fidelity does not demand we live according to a false pretense.
You are not morally allowed to let someone else abuse you with no realistic higher purpose. If he beat you or abused you, for instance, you might still be married, but you might have to recognize he was a serious threat to your well-being and, as this is a near occasion of serious sin for him, a grave threat to his own soul. If this were a permanent state of affairs, then you would be bound to at least seek a civil separation, and sometimes even to pursue criminal charges. This is particularly true if his repentence is most likely if you leave or require him to face justice for his acts before the day he stands before the Throne, and it is too late.
You cannot morally allow him to habitually use you as a source of serious sin, any more than you can stand by and allow him to use someone else that way. Even though you might still be married--if married with knowledge and intention to do right, and this wrong was his choice, and better was not beyond his capability--the Church recognizes that a civil separation or divorce can be a greater good than staying together, even when the marriage is valid. Likewise, if he were to be unfaithful in a way that would be dangerous to your health.
If there were kids, then you are even more bound not to allow him to abuse you or the sanctity of your marriage. To allow him to abuse these would be to allow him to abuse your children. To know your mother is being abused and to have nothing done to protect her, this is an abuse. To be forced to watch this is even worse. To grow up seeing a twisted version of marriage being passed off as the real thing is an abuse. Certainly you would not be teaching your children what the Sacrament of Marriage is...and do not think your life would not speak more loudly than your words. So you could be morally bound to get out of the situation in that case, too. Depending on the situation, you might be ethically bound to seek a divorce in order to force him to support you and them, as justice demands. God requires us to live according to the truth, not according to a lie.
There are cases in which one spouse might tolerate gross injustice or infidelity from the other, in the interest of repentence. This is a great act of charity, and very admirable. There are cases, though, where repentence is not a realistic goal. In that case, protecting yourself and removing yourself as a near occasion of sin for him can be a moral imperative. You might be less virtuous in staying than you would be if you left.