I'm an asylee, but married to a wife form different nationality, can she keep her original passport and visit her country?

I have granted asylum 3 months ago, and everything is OK. I have been married before applying for asylum in US courts, so I can bring her here legally. She is from different country than I am, and she has no problems in her country. My question is: What kind of visa they will give her? in case if she chooses to go to here country for short visit (or even other countries), does she need "refugee travel document", like I am, or she can use her original one? If there is a source where I can get further info, it would be great Thanks