What is acceptable proof?

Shortly after my 21 year old son graduates from college this December, I plan to initiate divorce proceedings against my husband who has cheated on me with numerous women during our entire 23 years of marriage, including fathering a child with one. In a couple of weeks, my son and daughter will both return to college in another city, which will leave me in the house alone with my husband, who has proven that he will lie on anyone if it means saving himself. I know that he will begin staying out late or all night once the kids are out of the house. I plan to document those times. However, I definitely know that if we end up in a courtroom, he will certainly lie and say that I stayed out all night! How on earth do I prove otherwise? I know that he will do this because I have learned that he lied tremendously on his first wife during their divorce hearings. What kind of things can I do to prove that I was at home at a time when he will say otherwise, particularly when I am alone? What does the court accept as proof of something like that, or does it just rest on creditability of the two parties? There are many provable instances of his propensity for lying, which cannot be said about me. I feel a little stupid asking this, but I know that I need to think about this before my kids leave for college. Thanks!

My non-professional opinion:

Do you have a LAN line phone? Maybe you could bring in your phone bill showing calls made from the house (where you are).

Document the times he leaves the home and stays out all night. You may do so by keeping a detailed journal. You may also want to consider hiring a PI to follow him and take pictures to document his whereabouts.