Menéndez March's partner, who is from Mexico which is a visa waiver country, was granted a six-month critical purpose visa based on his relationship with the politician.
His partner was approved for an expression of interest in December then had his visa granted in January.
One of the requirements of the visa is the couple must be in a "genuine and stable relationship".
National's immigration spokeswoman Erica Stanford questioned whether the visa should have been granted given the couple lived in different countries.
Menéndez March said he had been with his partner for more than two years and they'd spent a substantial amount of time together on his trips home so news the visa was given the all-clear was "no surprise".
Menéndez March, who is the Greens' immigration spokesman, said he hoped the focus would return to policy gaps which led to immigration discrepancies.
"We need to work collectively to honour the real trauma that people from the migrant community communicate to us and that's an ongoing piece of work."
Stanford stood by questioning whether the visa should have been approved.
"That's the job of an Opposition MP is to always make sure that there hasn't been any special treatment."
Stanford said she was still surprised the visa had been given the all clear.
"I am surprised that they've deemed short holidays - self-described by Mr Menéndez March to be holidays - to be conventional living arrangements.
"They've got more information than I do, clearly."
At the select committee meeting Stanford said one of her constituents was in a similar situation but their partner visa had been declined.