If wife and husband has two separate email address each belongs to each others personal/private and both is used in Stack.

In such case both becomes as 1 user account under Stack?

No. This happens only if you've logged in as 'husband' & add the 'wife's' email address to the husband's login credentials.

Going by your logic, all gmail accounts should've been merged into one :|

had two separate Stack Exchange accounts. One was work related, the other was for personal use. For some reason, StackExchange merged those two accounts as one

No. This happens only if you've logged in as the first user & add then added the second account's email address to the first account's login credentials.

Both my wife and I have our own StackExchange accounts, each registered to a different email address. Would these accounts be merged if we use the same network or computer?

Typically, they won't be merged unless you proceed to do the steps as mentioned above.

If so, how can we let StackExchange know that these accounts should be separate?

Don't login from two accounts at the same time.