Shared Calendars Exchange & IMAP

Upfront let me say that I do not have any technical/IT background. Just an average guy trying to figure some stuff out. Please excuse me if I incorrectly state some terms below.

I'm co-founder of a small company (Company A). It's still in it's 1st month of operation. My business partner is part time involved in A and part time involved in another company (Company B). I need to be able to see/modify both of his calendars (in 1 place) and he needs to be able to see/modify mine. 

Company A's domain is registered with Zoho and email domain is IMAP. Company B is using Exchange. 

Company A has just signed up for Office 365, but with IMAP email and Company B was already using Office 365 Exchange.

I'm just learning that IMAP does not allow calendar sharing. There's no option to change anything in Company B because it's already established with employees etc, so whatever changes need to be made, it has to be in Company A.

Can anyone help me with this conundrum? I appreciate any help.