This is not 2-phase, it is split-phase. Think through how that works.
Imagine if you will, two 100A transformers separately service two completely separate 120V systems.
What's the capacity of these together? 200A @ 120V, obviously. So now let's bridge them together so we have 240V end to end.
What's the capacity of these together? Still the same 200A@120V, obviously, since all we've done is bridge them. But what's its capacity @240V?
Now here's the 100-amp question. Do these capacities share or stack? Or does one take away from the other? If the upper transformer is supplying 120V at 70 amps, how much 240V can it also supply without exceeding limits of the transformer?
Think it through.
In practice
Now in practice, those two transformers are constructed on a single frame. But they are indeed separate secondaries, just like the diagram shows. They can be wired with the secondaries in parallel, in which case 200A@120V is what you get.
And, in practice, you'll notice that in the following drawing, the transformer is up on a pole and shared by several houses. The only way they'll sell it to you is 240/120 split-phase.
Now, you asked how you hook up 3 subpanels of 240V, 120 leg A, and 120 leg B, respectively. Assuming we're dealing with a 100A main supply, you can do this:
Mind you, this is exactly what you asked for, not what would be commonly done. Because of that choice, you wouldn't be able to support MWBCs or split-phase appliances (NEMA 10 or 14) out of the sub-panels. That may not matter if you don't have any split-phase loads, e.g. split-phase appliances are not sold in the Philippines since half the island has Euro style 240-only power. There may be other reasons for wanting to do this, e.g. putting whole-panel GFCI or AFCI on the sub-panel, sub-metering for tenants, a central shut-off for all electric heaters, switching part of household load onto a small generator or 120V solar, etc.
As you gathered from the earlier exercise, you cannot load all 3 panels to 100A. Either 100A panel can be loaded to 100 - (240A panel load).
You want 300A
Right off the bat, the power company's pole line from transformer to meter must be able to handle 300A, and that's not what they usually install, because they're not in the business of filling the sky with useless aluminum, and pulling another power drop is not that expensive for the rare customer who needs it.
Depending on your panel, upgrading to 300A is not as simple as swapping your main breaker for a 300A one. Very few service panels are listed for 300A. The chance of you having one is remote.
Typically, in this case, power companies feed two main panels from a single meter, and so you could slap a common 200A or 225A panel right next to your existing 100A panel without having to rewire it. However in that case you would not be able to feed 300A to each of three subpanels.
Getting split-phase out of the above
As drawn, you can't get split-phase out of any of the sub-panels because they are not 120/240 panels. That would require a fourth feed wire.
That's because hots, neutral and ground must source out of the same panel. You cannot feed out of 120V "A" and steal a hot from 120V "B". (we actually had a landlord ask to do that, to force tenants to split the cost of a water heater). You cannot feed out of the 240V panel and steal a neutral or use ground as neutral.
In that case, you'd either feed the split-phase load out of the main panel, or add the fourth wire and reconfigure any of the panels to 120/240 service. As a practical thing they probably started as 120/240 panels anyway, since straight 120 or straight 240 panels are rare.
