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:

• 10 Reasons the Jews are from Judah
• Things “On-Housers” Hope You never find out!
• The Full Restoration of Israel Series
• The Hidden Irony in Christian Replacement Theology
• The “Ephraimite Error”: Critical Errors
• Two House Theology – Wikipedia