No. In my opinion, it's not a good plan.
Yes, it will likely give you SOME results in size and strength since it sounds like you're pretty skinny, but it's not a good plan for maximizing results.
What's wrong with YOUR plan:
You work opposing muscle groups in the same day.
You (accidentally) use the same muscle groups on consecutive days
You don't allow yourself any breaks.
You don't have a core workout (100 sit ups every other day DOES NOT COUNT).
You don't have a back workout.
Your cardio is boring, and doesn't align with your weight training.
First off, Days off... You shouldn't weight train more than 5days per week. Your body needs time off to repair and build. Hitting muscle groups twice a week for prolonged time can limit your development. Once a week with a small revist on another day is plenty.
Opposing groups: Break the body into opposing and complimentary/supplementary muscle groups. Focus on one major group and one complimentary group per day. For example, your plan uses the chest and biceps on the same day. Triceps supplement the chest, i.e. you can't bench press without using your triceps, so you'll inevitably work your triceps that day. HOWEVER, triceps OPPOSE the biceps, so you'll be spreading yourself too thin to work all 3 groups effectively in one day. Plus, you do triceps the day after chest. On day 2, you've already worn out your triceps on day 1 doing chest exercises, so you won't have the steam to really work them out.
No core: 100sit ups twice a week does NOT count as a core workout. The core is a very complicated system of many many muscles, 100 reps of the same movement will NOT effectively train even half of these muscles.
No backworkout: You need a back workout, the trunk is critical to having a strong core, and the lats are critical to overall body strength. Trunk opposes the abs, lats oppose pecs/chest. Your program neglects half of your torso.
Boring Cardio: Jumping rope for a half an hour will be boring. It sounds like you're interested in boxing... Try kick boxing. Mix in Muay thai kicking and knees with a good upper body technique and you'll get a great cardio workout, as well as a GREAT core workout. Mix up your cardio to keep yourself motivated and interested. Warm up with jumping jacks and mountain climbers, then do some heavy bag work, then some shadow boxing, spot jumps, wall jumps, jogging, rowing, cycling, etc etc. Cardio should last 20-30min, but that doesn't mean you have to do the same thing for the entire time. Just keep your heart rate up and change exercises quickly.
A much better plan for muscle gains:
Monday: lats, trunk, and biceps
Tuesday: Chest, abs, and Triceps
Wednesday: Traps, delts, and forearms
Thursday: Quads and glutes
Friday: Hamstrings and Calves
Do cardio after your weight training each day, but mix it up to keep yourself interested.
To build bulk, move heavy weight. To maximize your gains, cut your body into quarters (upper front and back and lower front and back), do heavy weights with upper rear then lower front in the same week, then the next week do heavy with upper front and lower rear, i.e. Monday and Thursday are heavy one week with lats, trunk, and biceps, and quads and glutes, then the next week go heavy with the chest, triceps and abs and hamstrings and calves on Tuesday and Friday. The next week just go heavy on Wednesday and hammer your traps, delts, and forearms. Every day you go heavy, take the next day kind of light.