The low income children's healthcare program here in Texas is called CHIP. Depending on your husband's earnings, y'all may be over the income limits and need to purchase insurance on the open market. I would start with CHIP and ask if they have suggestions for private pay insurance for folks who don't qualify for CHIP, if that's where you end up.
If you are eligible but have trouble getting your eligibility confirmed - you should talk to folks at legal aid or the Center for Public Policy Priorities. There are all sorts of issues with people having long delays due to Texas eligibility system's really stinking it up. Still I thin CHIP covers more kids in TX than any other insurance program. If you are eligible for Medicaid (lower income guidelines than CHIP) - they should be able to figure that out in your application for CHIP also.
Depending on what city you are in, there may be local clinics that are reduced pay or free - El Paso is the best I believe in covering children. Austin has a clinic called the People's Community Clinic you could call. Other cities I don't know so well.