What is done in love and without injury to your faith is generally fine. You don't say how old you are, but dating leads to serious relationships, engagement and marriage sometimes...(she says wisely). The Church foresees that even the dating part can pose challenges to your own faith--for instance, will your friend invite you to synagogue? Would he come to church with you? The answer "Yes" poses one set of questions; "No" poses another.

It can be especially enriching to date someone who is Jewish because, as Pope John Paul II said, "They are our elder brothers in faith." 

I would adopt an attitude of cautious optimism and move forward.