In the phrase above, what do they mean? Neither is found in a dictionary.
The sentence is said to translate to "The pair would not divorce because of the children".
2 be for the sake of ...
Kànzài nǐ bà de miànzi shàng, wǒ yuánliàng nǐ.
For the sake of your father's face, I forgive you.
2 名 情分; 情面
Which basically translates to feelings, sensibilities, affections.
for the sake of, for sb.'s/sth.'s sake
wèile ( ... de lìyì) 为了(…的利益) ; kànzài ... de fèn shang 看在…的份上
We must do this for the sake of the children.
Wèile háizi, wǒmen bìxū zuò zhè jiàn shì.
So now we have our 看在…的份上 construct meaning roughly the equivalent of "for the sake of, for sb.'s/sth.'s sake" where 看在 means "for the sake" and "份上" means feelings or sensibilities.
You can stick anything in the middle for the "who's" sake/sensibilities/feelings/etc.
Some examples: (from Oxford)
for God's sake
for Pete's sake!
for heaven's sake
I would parse this as 看, look, 在, at, preposition (or result complement), 孩子, kids, 的, possessive particles, 分, separation, 上, a postposition forming a "prepositional sandwich" with 在. So literally, I would translate it to "Looking on the side of the children", which I would then render more loosely as "for the children's sake". So neither of those should be single words, they should both be two words,
kàn zài and
Then again, this is just my two cents, and I'm neither an expert, nor someone who's ever seen these two character combinations before, nor a mother-tongue.