According to Bryan A. Garner, in the Oxford Dictionary of American Style and Usage*:
"For joint possession, an apostrophe goes with the last element in a series. If you put an apostrophe with each element in the series, you signal individual possession: E.g:
John and Mary's house (Joint)
John's and Mary's houses (Individual)"
Of course, Garner's examples are different from yours in that you are referring to only one house. Nevertheless, if there is only one house but two owners, the apostrophe would normally go after the second element, according to Garner.
The Grammar Exchange responded to a similar question, which is in the Archives under "possessives." Here is that question along with its answer:
Q: Which one is correct, and why:
1) Mary and John's car, or
2) Mary's and John's car?
A: Mary and John own or use the car together, Example 1) is appropriate in your sentence:
a) Mary and John's new car was stolen from their driveway yesterday.
Conversely, if Mary has one car, and John another, you could use Example 2) in your sentence
b) Both Mary's and John's cars are in the shop.
Or, you could say more comfortably:
c) Mary's car and John's car are both in the shop.
In joint or group possession, add the possessive marker only to the last noun of the unit. The concept of "unit" is important here:
d) Hilary Rodham Clinton and Bill Clinton's daughter Chelsea graduated from Stanford University.
In individual possession, add –˜s to each noun:
e) Hilary Rodham Clinton's and Bill Clinton's different lives now keep them apart in different cities.
While it would be usual to use "Tom and his brother's house" in your sentence, you could emphasize the separateness of Tom from his brother (and possibly some antagonism) by using "Tom's and his brother's house."
*The Oxford Dictionary of American Usage and Style by Bryan A. Garner. Oxford University Press. 2000