如果只是在墨西哥靠岸的话，你父母都有有效护照和美国多次往返签证的话，是完全没有问题的。多次往返签证可以保证你能在结束旅程后再次进入美国国境。像你的情况，你可能不想改变现在I94的期限，所以你可以选择不放弃I94。墨西哥为了促进旅游并不要求办理临时墨西哥签证，还是很方便的。请参考下面墨西哥领事馆的回信。
IMPORTANT CHANGES TO MEXICAN VISA REQUIREMENTS STARTING MAY 1ST, 2010
With the purpose of simplifying and promoting traveling to Mexico, starting May 1st, 2010:
All foreign visitors who travel to Mexico as tourists, on business, or in transit to another country will not require a Mexican visa, regardless of their country of citizenship, as long as they have a valid passport and a valid US visa (which must be presented before Mexican Immigration authorities at the Port of Entry).
If you have any questions please contact our Visa Department at visas@mexicomiami.org or at (786) 268-4900 ext. 4906.
PASSENGERS ON BOARD OF A TOURIST CRUISE
Passengers embarking on tourist cruises do not require a visa to visit Mexico regardless of their nationality; they only need to present a valid passport at the port of entry.
CRISTIAN FLORES
CONSULADO GENERAL DE MEXICO
DEPARTAMENTO DE VISAS
5975 SW 72nd St (Sunset Drive)
South Miami, Fl. 33143
Tel: (786) 268.4906
Fax: (786) 268. 4903
