JewsAndJoes.com defines it this way:
What is “Two-House Theology”? Well, first it is known by several names, both positive and disparaging. It is called the “Two-House Teaching”, the “Two-House Doctrine”, the “Two-House Ideology”, the “Two-House Movement”, the “Two-House Heresy”, the “Ephraimite Movement”, the “Ephraimite Fallacy”, and the “Ephraimite Error”, but we like to call it “the Two-House Reality”! And Zechariah 10:6 (see below) depicts this reality of two peoples, both “Jews” and “Joes”, in a prophetic and unconditional Last-Days (End-Times) scenario. It is only one of those frequently referenced by advocates of this great reality (see more verses here).
“And I shall strengthen the House of Jew-dah, and I shall save the House of Joe-seph. And I shall bring them back, because I have compassion on them. And they shall be as though I had not cast them off. For I am יהוה their Elohim, and I will answer them.” - Zechariah 10:6
For the full article, go here: Two House Theology (Reality) defined and defended.
For more details on Two House Theology: