After a 40-min weight training session that tore through every fiber of muscle in your biceps there begs the question: should you finish your workout with a 20-minute run or is that going to take away from your Arnold-like gains? The answer is yes, it will take away from your gains and no, you don’t look like Arnold yet: but do you really care?
Sure, everyone cares that they don’t look like Arnie pumping iron, but at the end of the day it falls back to what you are trying to achieve. If muscle hypertrophy (fancy way to say building muscle) is your goal then steady state cardio right after your weight session would most likely take away from your gains. This is the same case when it comes to strength training, mixing cardio and strength in the same session means that you may not get quite as strong or quite as fit as you would have had you only done one of them. So if strength or hypertrophy is your sole goal then try not doing any cardio in the same session, or ideally on the same day.
If your better half has mentioned that you have a gym curfew and that more love is needed in place of exercise, then think about prioritizing your type of exercise (as well as partner type!). The neediest one goes first: so if building up your cardio is more important, then put that before the weights. Whichever you spend time on first will get the better training stimulus compared to the latter, once you are physically and mentally fatigue: your drive will diminish and you won't push yourself as hard.
Realistically, if you are not training to be the next strongest man on earth and at the end of a session you feel like throwing in some additional mileage on the treadmill then do it, this keeps your head in the game and means you are more likely to adhere to your training.