"The nurse practice acts state that only nurses can give meds." Actually each state has its own nurse practice act and in some states the principal can administer medication or direct another employee to administer. You would want to check the Board of Nursing and the state's education code for guidance on that issue. Another resource would be to contact your states school nurse consultant.
If a child qualifies for a Section 504 plan, a school cannot refuse to give medication and cannot insist a parent come to school to administer.
Certainly any individual can be sued for harm (I am not a lawyer, but see In Schwab, N.C.& Gelfman, M.H.B., Eds. Legal issues in school health services. North Branch, MN: Sunrise River Press). However, your district is required to provide training for anyone administering medications and should have a policy and procedure for administering medication and its documentation. Most states require a doctors order for a nurse to administer a medication in school, and most school districts will not administer over the counter medications without a doctors order, especially with the increased attention reactions such a Steven-Johnson Syndrome are getting.
Your husband, the 4th grade teacher, should find out if the health department nurse is contracted for specific services (such as those you mention) or if she is contracted to provide health services, or is contracted to provide consultation to staff. I would think talking to her might be a good place to start. Asthma and cardiac meds are nothing to be casual about and could definitely cause harm, and even death, is administered inappropriately. In some states his actions would be considered practicing nursing/pharmacy without a license. In any event, there is an accountable individual in his district (assistant superintendent, superintendent, Director of pupil personnel, or special ed director in most districts) who is responsible for student health and he should find out who that is and find out the district's position.
Quote from hypnotic_nurse
When my kids were in elementary school, we were not allowed to send medicines to school. If the child had to take a medicine at school, the parent had to show up and give it.