If you look at the consistant use of the word "house" in the text it means "household" or "family" not a place or institution. What Paul is talking about is the local family of God, especially since there were many local representations of the "household of faith". It was in the local "household", the assembly or company of those called out by the Holy Spirit, that the truth, the the word of God, was maintained and propagated by the Holy Spirit through the gifts given to the local household of faith.
There is no "house" there of any kind. "House" is "oikos" or I beleive "oikia" at times. The word there is "ekklesia", that relates to community or assembly.