You didn't mention what day you're traveling, which can make a difference in your route but some genral info is:
Saturdays:
CO: Has 2 direct flights from Houston into Roatan, where you can catch Atlantic Air into Utila.
DELTA: Has a direct flight from Atlanta into Roatan, where you can catch Atlantic into Utila.
TACA: Has a direct flight Houston into Roatan, but I think it gets in too late for the connecting flights? Anybody with intel on this?
SUNDAY: Taca has a direct flight Miami into Roatan, but there are no connecting flights to Utila on Sunday's. There is however, a charter service on a Cessna called 'Roatan Air'. They can be booked through Maya Carribbean in San Pedro Sula.
WEEKLY:
CO has a direct flight from Houston to San Pedro Sula & American has a direct flight from Miami into San Pedro Sula. Sosa & Atlantic can get you to Utila from there, but it is a connection through La Ceiba, so an extra stop.
Sosa also has flights from Roatan to Utila as an alternate to Atlantic, but check the timing because it's a tight connection with some of the Roatan jets, and clearing customs & Img is an 'interesting' experience.
I always cheat & fly into Houston the night before, have dinner with friends, then board the jet fresh in the morning... but that's just me.
Hope the info helps. Hear CO & Delta are may have put on more flights, so check their time tables. Airport designations are RTB & SAP for roatan & San Pedro.