Some will argue that there are many biblical examples of marriage relationships that we would find strange or even objectionable. Christians cannot claim that heterosexual monogamy is what the Bible teaches or that there is an exclusive biblical model. If we actually followed the Bible we would embrace a similar range.
There are many different arrangements including:
Polygamy – men having more than one wife. (Many examples including Abraham, Jacob, David Solomon.)
Levirate marriage – the brother of a deceased man who had not had children, marrying the dead man’s wife
Required marriage after a rape (Deuteronomy 22:28-29)
Concubines – essentially mistresses; sexual partners but not wives. (There are many examples including Abraham, Jacob, Caleb, Gideon, Solomon who had 300 (1 Kings 11:3)!)
Wife allows her husband to sleep with her slave (e.g. Genesis 16: Sarah offers Abraham Hagar; Genesis 30:4-5: Rachel gave Bilhah to Jacob)
Wives captured in war (Number 31:1-18; Deuteronomy 21:11-14)
The Bible does not endorse all of those different arrangements.
Some were clearly human inventions, not God’s design, and in that sense were sinful. The fact that they exist does not mean they were approved by God and are therefore a model for us.
Often the inadvisability of these arrangements is seen in their negative consequences – jealous wives, etc.
In all that diversity, there is not a single homosexual relationship.
The Bible is an utterly heterosexual book. Even the depraved examples do not go as far as homosexual relationships.
The explicit biblical model is actually heterosexual monogamy
The order established in the Garden of Eden was heterosexual monogamy. God created men and women for each other; “male and female He created them” (Genesis 1:27). The creation of Eve for Adam set a pattern expressed in the biblical conclusion:
Genesis 2:24
For this reason a man will leave his father and mother and be united to his wife, and they shall become one flesh.
Note that “man” and “woman” are singular and that it is in this relationship of leaving and cleaving that the sexual relationship is ordained.
This model is reinforced by Jesus and by Paul when they quote this passage in Matthew 19:4-6, (Mark 10:2-9) and Ephesians 5:31-32.
Note too that no other model is endorsed by either Jesus or Paul – only heterosexual monogamy.