If you are a US citizen, and assuming you are 21 or older, you may petition for your parents, and they will be obtaining a permanent, 10-year green card, as immediate family members. After they receive a green card, they have to start making US their permanent home. Absences of 6 months or more will raise questions, and may subject them to questioning as to their intent to immigrate to the US. So be cautious about that, and always remember, it is all about their "intent." They have to prove to the Officer that when they are returning from an extended travel, that they do intend to make US their permanent home. Also, after they qualify and become citizens, they can live anywhere they want in the world.
Contact immigration attorney Gintare Grigaite, Esq. at 646-407-2331, located in New York and New Jersey. Answers on AVVO do not constitute legal advice and do not form attorney-client relationship. Always consult an attorney for a legal advice.
It appears like they should not proceed with lawful permanent resident status processing. It seems that they plan to keep their permanent residence outside of United States.
This means that they should consider a multiple entry B2 visitor visa. However, they should be careful not to abuse the privilege of visiting United States.
For more information, I strongly recommend an appointment or teleconference with a competent and experienced immigration attorney, who can spend enough time to carefully answer all of their concerns.
This is general information, not legal advice, and does not create an attorney client relationship.
Good questions, best asked in private with an attorney.
Bottom line, the GreenCard is a PERMANENT RESIDENT card ... they need to be living in the US MORE than they live someplace else.
I recommend stays outside of the US be less than 90 days ... with an occasional 180 ... don't believe things you read about 1 year, or 2 years ... every time they come through the border they will be given a hard time.
Talk to a lawyer for more details.
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FORMER IMMIGRATION LAW PROFESSOR -- LEGAL DISCLAIMER: This answer is offered for informational purposes only. It does not constitute an attorney-client relationship.