Family, Other Spouse of American; both living abroad

[Lety]

I am Mexican and currently have a tourist laser visa issued for 10 years. My husband is both Mexican and American. He just found his American passport and renewed it with no problem. His mother is American living in Mexico and forgot that a long time ago she had gotten a passport issued for him. We got married almost a year ago in Tampico, Mexico and in a month we will move to Matamoros, Mexico (border with Brownsville, TX) because he was transferred. I want to know if I have to do something about our marriage and myself at the US embassy and if this will be beneficial. In the future we would like to move to Brownsville because the city is much better and rent is not so expensive. Both our jobs are in Mexico right now. I also want to know if I could work in Brownsville in case we moved.