Is a diploma from a Christian Private School as good as a public high school?

I have a gf who's probably pregnant and she dropped out of high school and started attending a private Christian Academy and doing their home schooling program.Unfortunately she couldn't keep up with the monthly tuition cost and has been out of school for half a year. She wants to finish her education by doing the private home schooling through the private Christian Acadamy because she despises the public high school. Now a well respected teacher of ours has told us that getting a diploma from the state is better than receiving one from a private Christian Academy, is this true? I really want her finish high school through the state alternative program which will allow her to work in a clroom with few people, everything will be online so she can work on her clwork at home as well as finish a year in as little as a week or month, and she may finish early. I'm really pushing her to do this for our soon to be born kid, but is it the right thing to do? Should i let her finish highhschool at the Christian Acadamey?? Would colleges and well respected employers accept employers take the diploma from a christian acadamey? (sorry for any typos and grammer mistakes, i used the spell checker on here... big mistake)