The gemara in Kesubos 8a says that the בנין עדי עד (in one of the brachos of sheva brachos) refers to Chava. Additionally, the text of the beracha implies nothing about it referring to a home. So why do people say divrei torah and use this as a reference for the couple to build an everlasting home?
Actually, it's Rashi, not the gemara, that says that... Ultimately, people use it because it's nice, not because it's 100% accurate vis a vis dikduk and the gemara. Lots of derashot do this - they take liberty in deviating from the peshat for the purposes of providing a nice message...
After further thought, the "Binyan Aday Ad" is referring not to Chavah, but to Womanhood (because Chavah would become mortal). The term Binyan refers to the shape of a woman, which is not an exclusive trait of Chavah. This means that the bracha would therefore be a reference to Marriage and not just Chavah being made for Adam. Contrast this to us referring to a "Bayis Ne'eman BiYisroel" - the word bayis doesn't appear in our bracha.
The bayis is a result of the binyan of the ishah being referenced in the bracha. Bayis ne'eman is stating the hope that the familial line being instituted by the bride and groom will not fail - that they will have children and those children will go on to have children, "maintaining the house." We only refer to the woman's role in conception and childbirth obliquely when we gloss over the meaning of the bracha to wish them a Bayis Ne'eman, but it's still there.