There are two major lines of the Dunham family in America. One descends from Deacon John Dunham of Plymouth Colony and the other is actually a Singletary family. Ancestry.com has Edward & family as descendants of Jonathan SINGLETARY (1639 - 1706, Woodbridge, Middlesex, NJ).
Edward Marion DUNHAM (Sep. 1864, Logansport, Cass, IN - 12 Apr. 1942, Logansport, bu. Davis Cem.) m. 7 Oct. 1886, White Co., IN, Electra Arvilla SHULL (24 Jan. 1869, Burnettsville, White, IN - 18 Oct. 1941, Cass Co., IN).
The line as listed on Ancestry is
John Wesley DUNHAM (1832 - 1902) & Sarah E. BURN[E]S (1844 - 1932).
David DUNHAM (1762 - 1840) & Hannah BRUM[M]AGE (1783 - 1844)
Elisha DUNHAM (ca. 1730 - 1783) m. 20 Je. 1752, Woodbridge, NJ, Elizabeth FREEMAN
Joseph DUNHAM (1700 - 1771)
David DUNHAM (1673 - 1753).
Jonathan SINGLETARY alias DUNHAM.
Some descendants of David, b. 1673, went to Canada as Loyalists during the Revolution, per Kenneth Royal DUNHAM's Dunham-Singletary Genealogy, 1987.
If you Google names this way: "Elisha Dunham" +"Elizabeth Freeman," Google will provide information on most of the couples in the lineage.
I have not verified the above line. I descend from the Deacon John Dunham line through John, son of his first wife, and a third John. I also have a Freeman line with five Edmunds in five generations in a row, but they were from Pulborough, Sussex (later of Sandwich, MA), and online sources say your Elizabeth's line came from Cambridge and London.
You can find information on RootsWeb Family Trees / Advanced Search. If you have a living male relative with the surname Dunham, you could verify this with a Y-DNA test. There is also an autosomal DNA test that anyone can take to find relatives who have also taken the test .
Google FamilyTree DNA and 23andme for more information on the tests.