My husband is an american guy and I´m mexican living in my country and thinking in bringing him here to live. I plan to open a business in Mexico and I don´t want to pay taxes to the united states.

Anyway I want to be free going there for long periods, and back to my country.

The other thing is... my husband could say he is married and get some refunds if he says that he is married.

So, should I keep my B1 tourist visa, or should I fix my papers?

Thanks

First off... if you managed to get a green card... they would cancel it if you spend long periods out of the USA... too many people were getting it for convienience and living elsewhere... so they tightened up the regulations so the people that intend to spend most or all of their time here get the limited numbers available.

It doesn't really matter what type of Visa you have for tax purposes. If you live outside the US you don't even need a visa and can still file a joint return with your US husband.
Since he is married he needs to file as such, he cannot file as single.
You would have the option to be treated as resident alien for tax purposes. That would mean you would have to report worldwide income as well, but you get the foreign earned income exclusion (exclude up to $97,600 in 2013) or the foreign paid tax credit.
If you don't want to be treated as residnet alien, your husband would need to file as married filing separately, but he can use an exemption for you if you don't have any US source income.
Read publication 519.

That's for the tax side of it. Your other issue is with travel, so if the visitor visa is not good enough, you would need to apply for a spousal visa/green card, but as smoothy said, that's not that easy.

Note that if you file jointly and claim the Foreign Earned Income Exclusion (Form 2555), you can exclude your business income tax purposes, but would still need to pay self-employment tax at 15.3%.

You will need to model the return several ways to see which way is best.