I am sorry to hear about your situation. This must have been quite a shock.

Islam allows for you to stay together and also allows for separation. It is between you and him. Sometimes married couples confront major challenges and emerge stronger, and sometimes they don't.

It is a good time for soul-searching and considering what you want for the rest of your life, as well as any circumstances (such as how well you get along, whether you have dependent children, whether you are financially independent, and so forth).

There are hadith which discourage divorce in favour of staying married, but it is a recommendation not a requirement. Perhaps, in part, because divorce often puts women in a more difficult situation financially and otherwise. 

It is unlikely you will have the same relationship as you had before, but it is possible for you both to heal from this breach of trust and come to a "new normal"; however, this takes time and effort. Nothing ever stays the same throughout life; we often have to adjust to new circumstances. 

He does have an ethical responsibility to act as a father towards the children and be present in their lives - it's not their fault this happened - but this is a different matter.