Marriages that occur in the Phillipines are recognized by the USA government, but you, being a non-USA citizen, I believe, will still need your passport and a visa to come to the USA with your husband.
It's my understanding that applications for USA visas by new wives of American men are routinely granted, unless there is a criminal record or medical problem (tuberculosis, for example) that would cause your visa application to be delayed or denied.
The USA Embassy in the Phillipines can best advise you, because I am not 100% certain if my remarks are totally accurate.
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