Greencard through marriage while in an H1B visa

[rincha]

Hi,

I am a Spanish citizen working in the United States under an H1B visa, which expires in Oct 2013.
I am marrying my american fiance this year and I would like (and need) to start applying for the greencard as soon as I am married.
My question is:
If I continue working for the same employer, can I travel internationally under the H1B visa while I wait for my adjustment of status?
I will definitely get married before the end of my H1B visa permit but I still want to be able to travel outside of the country.
Thanks a lot

[immihelp]

Read http://www.immihelp.com/greencard/ad.../eadap-hl.html

Even if you can't travel on H1B, you can still travel using advance parole.