You can acquire a green card through marriage, but not US citizenship.
(213) 394-4554 x0 Mr. Shusterman is a former INS Trial Attorney (1976-82) with over 35 years of immigration experience. His response to your question is general in nature, as not all the facts are known to him. You should retain an attorney experienced in immigration law to review all the facts in your case in order to receive advice specific to your case. Mr. Shusterman's statement above does not create an attorney/client relationship.
If you apply for lawful permanent resident status, remain in the U.S., and never apply for naturalization, then you can retain your Czech Citizenship. If you leave the U.S. with the intention of not returning and stay away for six months, then this may result in the loss of lawful permanent resident status.
If you wish to keep your lawful permanent resident status, then you need to consider whether you should become a naturalized U.S. Citizen or apply for a re-entry permit. A foreigner may lose their lawful permanent resident green card status if they remain outside the U.S. too long.
If you have concerns, I strongly recommend an appointment with a competent and experienced immigration attorney.
This is general information, not legal advice, and does not create an attorney client relationship.