how can I get the green card or permanent residency?

If on the basis of your having two children in the US, please note that US immigration laws do not allow permanent residence based upon having young children born in the US.There is the so-called ten-year green card, but that requires 10 years residence, good moral character, and that you prove exceptional and extremely unusual hardship to the children if you have to leave the US. In addition, that type of application is for people who are illegal, and is requested before an immigration court, not U.S.C.I.S There are many difficulties in getting such a case before the immigration court.  Due to the limitations of the Lawyers.com Forums, Alan Lee, Esq.'s (the "Firm") participation in responding to questions posted herein does not constitute legal advice, nor legal representation of the person or entity posting a question. No Attorney/Client relationship is or shall be construed to be created hereby. The information provided herein by the Firm is general, and requires that the poster obtain specific legal advice from an attorney. The poster shall not rely upon the information provided herein as legal advice nor as the basis for making any decisions of legal consequence.