Alex, the marriage of two Jews, two Muslims, or even between a Jew and Catholic is still a valid marriage.
What it lacks is the Sacramental Grace that is found in the marriage of two Baptized persons.
The Sacramental Grace of any form is a Sanctifing Grace, that brings one closer to God and is a means to salvation. This is present in a Christian marriage, but that not specifically what binds a marriage.
You can see that when Christ was talking to unbaptized Jews about the wrongs of divorce. He was certainly not stating that their marriages were all false (least off all the marriage of His own Earthly parents).
In fact, He was stating just the opposite. That those marriages, yes the non-Sacramental marriages all around him, were sacred to God and binding to both parties.
That is why the Church recognizes non Sacramental marriages as binding, and thus an annulment is required in cases of divorce and remarriage.