How can I apply for permanent US residency when I am dependent on my husband's E-1 visa?

My husband is a Honduran national and I am from the UK. We moved here to the US on an E-1 visa. But having to constantly shuffle in and out of the country in order to keep our I-94 current, and also having to sweat bullets every time we need to renew our E-1 visa at the US Embassy in Honduras every five years (I'm always afraid they are going to find some insignificant reason to deny our visa)... well, it's getting a bit much... How can I find a path to permanent US residence from where we are now??