Gluadys,
As you said you are familiar with liberal Christianity, can you explain to me what exactly makes a person liberal? Also, is it purely doctrinal, or a combination of doctrine, this 'higher criticism' and moral/social issues?
As I said above, I don't think there is much in the way of doctrine that characterizes liberals as a group. They do tend to reject recently-developed doctrine such as biblical inerrancy, but there is no real consistency on traditional doctrines like the virgin birth. Probably what characterizes liberals in that regard is the level of tolerance for diversity of belief. The differences that exist are never a source of internal controversy.
Another characteristic that strikes me is that there tends to be more emphasis on Jesus than on scripture. Even out on the fringe where people deny his divinity, there is an understanding that Jesus is the focal point of Christian faith, a model and exemplar. But this is not to say the scriptures are unimportant to liberals. The phrase I grew up with is that we take the scriptures "seriously but not literally".
A more characteristic difference is the tendency to emphasize social and structural sin as opposed to the conservative focus on personal morality. (Of course in the best of both liberal and conservative churches, both get attention.) But typically a liberal will be more concerned about the injustice of poverty than about abortion. Indeed, abortion would also be approached more through social than through moral categories. Justice is a strong focus in many liberal churches, and I have seen a great deal of increase in the understanding that justice and charity must both have a place in Christian ministry: that the charity-only model proposed in some churches is simply inadequate as a sufficient Christian witness.
As for "higher criticism" it is important to understand from the outset that the terms "higher" and "lower" used in the 19th century were not about ranking. "Lower" criticism was directed to study OF the text to determine from the archeological remnants of manuscripts as nearly as possible what the scriptural text is. Today this is usually called "textual criticism".
"Higher criticism" was directed to study ABOUT the text i.e. date & place of composition, authorship, to whom it was directed, for what purpose it was written, in what form it was written, what earlier sources it drew from, what subsequent editing it received and why. And more generally, how various separate sources were brought together to become the canon(s) we have today. Today, "higher criticism" has broken into several different fields such as "form criticism" "source criticism" "redaction criticism" etc. Liberals generally consider all of these to be simply academic disciplines addressing several questions about scripture. Conservatives often see them as an attack on the doctrines of inspiration and inerrancy.
I see a bit of a parallel to the issue of evolution here. Evolutionary creationists hold that we are both evolved and created beings and see no contradiction in this. Evolution is simply a mode of creation. Non-evolutionary creationists see evolution and creation as mutually exclusive such that they necessarily contradict. In much the same way, liberals accept the conclusions of higher criticism without rejecting the inspiration of scripture, whereas conservatives are unable to see a way to accept both, forcing a choice between modern biblical scholarship and their theology of scripture. Interestingly, the "higher criticism" controversy and the evolution controversy overlapped historically and it is not surprising that those who rejected higher criticism also rejected evolutionary theory and vice versa.
One final observation: when it comes to Christian education, there is very little difference between a conservative and a liberal Sunday school class. This is because the higher criticism-which is probably THE definer of liberalism-is academic. Most people don't encounter it much before college level studies. The typical fare in Sunday school is the content of scripture, not academic discussions about how scripture came to be. For the same reason, there is often little difference between the Sunday sermon in liberal and conservative churches -- except when the topic is one of the flash-points of controversy. But I expect that most of the time, it would be very difficult to tell if a homily on the Good Samaritan or Paul's letter to the Galatians came from a liberal or conservative preacher. We really do have a lot more in common than the issues that divide us.
One instance: Canada was recently host to the annual G8 & G20 meetings (and you may even have seen news reports about some of the events in my home town, Toronto). Preparatory to the G8/G20, the Canadian Council of Churches ("liberal") and the Evangelical Fellowship of Canada encouraged congregations to collaborate with other people of faith to hold interfaith dinners for Members of Parliament where the MPs would hear our concerns as people of faith about the needs of the world. There were two such dinners in Toronto. Both included sponsors from conservative denominations (Salvation Army in one case and an Alliance congregation in the other). I expect liberal and conservative Christians will continue to find more and more common ground with each other, and even with people of other faiths as in these dinners.