If I left the US for 16 months with a green card and didn't file any forms, can I come back into the US on some kind of visa?

As a matter of law, a green card holder green card holder who has stayed outside the U.S. for a continuous period of 365 days

Anytime a U.S. Permanent Resident leaves the U.S. for an extended period of time, the U.S. immigration service (USCIS) can deem that the person has "abandoned" their Permanent Residence ("Greencard"). The law doesn't really have a clearly defined period of time which would cause a person to lose their Permanent Residence. The USCIS usually presumes that any time a Permanent Resident has spent more than a year outside the U.S., that person has intended to abandon their Greencard. Usually a Permanent Resident who plans on living outside the U.S. for an extended period of time, applies for a "Reentry Permit" which allows the person to live outside the U.S. for up to two years without having abandoned their Residence. Your husband can rebut this presumption of abandonment of Greencard by showing that he had no intention of abandoning the Residence, and he intends to live in the U.S. permanently. He can do this by showing that he has ongoing connections with the U.S. that are stronger than his connection to the foreign country were he spent this time. For example, if he maintained a home in the U.S., had his bank accounts, etc., and had other family in the U.S., he can show that he has every intention of living in the U.S. permanently. Whatever he can do to show that his stay outside the U.S. was temporary and he intended to live in the U.S. permanently. So at this point he should just return to the U.S. with as much documentary proof as he can to show that he did not intend to abandon his Permanent Residence in the U.S.