In my mind, strength training must be part of any 'general fitness' program. The ability to handle your own body-weight is part and parcel of what it means to be fit. How much you can lift independent of your own mass, however is not. The strength training in this program will therefore aim to improve your strength to weight ratio rather than any absolute amounts of weight you can lift. Yeah, as you do get stronger you'll obviously be able to lift more, but try to focus on what you can do with your own body, rather than comparing any numbers you might get (in terms of weight and reps) with anyone else.
Because we're trying to develop functional body-weight strength and awesome endurance in an hour a week or less, you can rest assured that the strength training is going to be really short and really hard! In the template I'll give a couple of options--one that involves one 10-15 minute session a week and one that involves 2 sessions, each only a couple of minutes. I'd suggest using the longer session if you're still working to gain strength (i.e. if you're not as strong as you want to be) and the shorter sessions if you're trying to maintain strength and/or focus more time on your endurance pursuits.
The longer session is a modified version of Dr. Doug McGuff's 'Big Five' protocol and require access to a gym while the shorter sessions are body-weight only exercises that don't require anything that can't be bought off of amazon for $20 or found for free at any school playground.