Travel on conditional green card
If you're an immigrant to the United States with conditional resident status (which expires after two years unless you take further action) you have, during those two years, the same rights and responsibilities as a U.S. permanent resident. In fact, the popularly used term "green card" is often used in reference to both conditional and permanent residents. Among the rights enjoyed by green card holders is the right to travel outside the U.S. and, more importantly, be allowed back in afterward.
However, there are limitations on the travel rights of conditional as well as permanent residents. By spending too much time outside the United States, or giving up your home base here, you could lose your green card. And with any trip, you can be barred upon return if you've become "inadmissible."
There's an additional concern if you got your conditional residence based on marriage to a U.S. citizen and you'll be spending a long time outside the United States while your U.S. spouse stays behind. Such long separations may make it difficult to prove, as a condition of converting from conditional to permanent resident status, that your marriage is the real thing.
How Much Travel Is Too Much?
The U.S. government expects that green card holders will really live - that is, make their primary home in - the United States. In the government's eyes, someone who just wants to jet back and forth between international destinations, and not really settle here, does not deserve a green card. That conflicts with the desires of some immigrants, many of whom operate on the myth that as long as you return to the United States at least once a year, you can keep your green card.
That isn't true. In fact, technically speaking, you can lose your right to a green card after one day outside the United States, if you left with the intention of establishing a home elsewhere. This is referred to as abandonment of residence. Short trips rarely produce such extreme results, of course - a person returning to the U.S. after a few days isn't likely to face a lot of questions from the border official, who is the one who would have to raise this issue. But the importance of your intentions, and in some cases being able to prove them, is worth bearing in mind as you make your plans.
In fact, trips of up to six months don't usually raise many questions. However, if the trip lasts longer than six months, the questions you'll face upon return will get more probing. And if the trip is longer than a year, you'll raise a presumption that you've abandoned your residency, and have to work very hard to convince the U.S. immigration authorities otherwise. It's best to be able to show that you were kept away longer than expected, for example by a medical problem or the death of a family member. (Bring documentary proof of such events.)