Authorities said cellphones taken from the men when they were arrested last week include images of a large bridge in Zulia state, military installations and dilapidated oil refineries in Falcon state.
President Nicolás Maduro announced on Friday that an unnamed suspected U.S. spy had been captured, saying he was a Marine and former CIA operative in Iraq.
Venezuela also struggles to provide electricity to residents, especially in Zulia state, once a major hub of the nation's vast oil production.
The three Venezuelans accused of conspiring with Heath include a military officer, Saab said, adding that they helped him enter from Colombia.
The ex-Green Berets in Goudreau's force — Luke Denman Airan Berry Venezuela — have been sentenced to 20 years in prison.