Genealogy site where I can search for a family-tree with two particular surnames?

I hope you mean a Smith married to a Jones, not a Smith whose fourth cousin once removed was a Jones. No site in the 500,000 will do that last one, although Google might find them if they were on the same (massive) FTM report masquerading as a web page.

RWWC’s search engine allows you to specify spouse’s name – it can be given or surname. The LDS site allows you to look for marriage records. GenCircles has the spouse option too.

GenForum’s surname forums allow searches for the other name – in my example, you’d search the SMITH surname board for Jones, and vice versa. Ancestry’s surname forums do to; or you could search for both surnames across all boards. Roots Web’s mailing list archives recently upgraded, so you can search all the lists at once, so you could search for both names with the AND qualifier.

Illinois Marriages is sort of what you want, if your individuals were married in Illinois before 1900. So is the WV Archive marriage data base, again if you had ancestors there.

RWWC and LDS are below. Write if you want the other links.
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This is a long answer that I paste now and again to questions like yours.

The short answer to “How can I find my family tree?” is that if one of your great-aunts has spent 30 years researching it, AND has posted her research on the Internet, you’ll find it. If not, you will have to do the research yourself. It is not difficult, but it takes time. Most young people do not want to spend a couple of hours a week doing research, because it is too much like homework. So, you may want to skip the rest of this answer. If not, read on.

If your line has been “done”, chance are it is on one of these two sites. When you search, don’t fill in all of the fields. Start with given name, surname and birth year. Use (+/-) 5 for the birth year. Expect to spend 15 – 45 minutes on each. Neither has any living people, so don’t enter your own name.

http://www.familysearch.com
(Mormon’s mega-site. Click on “Search”, to start with, or “Advanced Search”)

Roots Web
http://www.rootsweb.com
and in particular,
http://worldconnect.genealogy.rootsweb.com/cgi-bin/igm.cgi
(Roots Web World Connect; 460,000,000+ entries, of varying quality)

Here are a few more. The resolved questions have lots of links and tips.

http://www.cyndislist.com/
(240,000+ links, all cross-indexed. If you want Welsh or Pennsylvania Dutch or Oregon or any other region, ethnic group or surname, chances are she has links for it.)

Ancestry.com
http://www.ancestry.com/
(which has free pages and FEE pages – so watch out)
and, in particular,
http://www.ancestry.com/learn/facts/default.aspx?ln=
Surname meanings and origins

http://www.tedpack.org/begingen.html
My own site: “How to Begin”

United States only:

http://www.usgenweb.net/
(Subdivided into state sites, which all have county sites.)
(The Canadians have Canadian Gen Web, by province)

http://ssdi.genealogy.rootsweb.com/cgi-bin/ssdi.cgi
(Social Security Death index – click on “Advanced”. You may find your grandparents.)

http://find.person.superpages.com/
(US Phone book, for looking up distant cousins)

United Kingdom Only:

http://www.genuki.org.uk/
(Biggest site for United Kingdom & Ireland)

http://www.freebmd.org.uk/
(Free Birth, Marriage & Death Records)

In the USA, some public libraries have census image subscriptions. Many Family History Centers do too.

This is a general hint: Even though you go in through YA Canada, YA Australia, YA UK or YA USA, all of the questions go into one big “pot” and get read by everyone in the world who speaks English. Most of the people here are in the UK and USA, but you sometimes get questions and answers from people who worry about kangaroos eating their roses. So, if you are asking about a specific individual, put a nation and a state / province. It will help people help you.