How multiple unfinished payments in single LN channel work?
The htlcs are just an additional output in the commitment tx which spends the funding transaction (as you described) 

So assume Alice and Bob have a channel of capacity 0.1 BTC in which alice owns 0.03 BTC. 

On chain you have a multisig wallet that has 0.1 BTC and offchain you have a commitment tx with two outputs. 

0.03 to alice
0.07 to Bob


Let's assume Bob wants to pay Alice 0.015 BTC or wants to forward an htlc through Alice of the same amount a new commitment tx is negotiated (by which the old one is invalidated) that has 3 outputs

0.03 to alice
0.055 to bob
0.015 htlc clsimable by Alice if she can show a preimage within a Timelock and afterwards by bob


Now if routing is successful alive provides the preimage and a new state is negotiated in which the htlc output is removed but added to slice balance resulting in

0.045 to alice
0.055 to bob


Otherwise the htlc is removed but the amount is added to bobs output. 

I omitted onchain fees for simplicity