That's a single battalion of 3 companies, not multiple regiments with several battalions each, so it's not even close to requiring RCT organization.
You could try to group it into Mech, vehicle, and infantry companies, with a few units out of place to fill in for the missing pieces, but in the field they'd likely be deployed as mixed companies ('Mech and vehicle lances, possibly with an infantry platoon or two in APCs) in an ad hoc formation, or else the 'Mechs deployed independently from the vehicles and infantry.
The organizational structure does not necessarily need to exactly match how the elements get utilized in the field, it's primarily for the streamlining of command and logistics (you don't need a mechanic for a 'Mech company, nor do you require a Mechtech for a vehicle company), but still easier to send in as groups than as diverse pieces grouped together tor a purpose. It would probably be extremely rare to see lances of mixed composition in any major House's military (despite being the most common OPFOR formation in MegaMek), but fairly common to find a lance or company of vehicles temporarily assigned to support/assist a lance or company of 'Mechs or vice versa.