Yes, we can do that. There’s a sketch for the emonTx (only the emonTx, not the emonPi) for “approximate” measurement of a 3-phase supply, and it can be set up as in your case to treat one phase as the neutral, so that the second phase is shifted 60° in relation to the first.
By “approximate”, I mean the emonTx has only one voltage input, therefore it is accurate so long as the voltages of the two phases you are using are the same (or the same within a error band that you find acceptable).
To do the measurement, you’d need an emonTx, a.c. adapter and two c.t’s, then if you want to log and record the data using emonCMS, you need in addition an emonBase and power supply. You can buy emonCMS on an SD card, or you can download it free of charge.
If you think (or know) the two voltages you use vary too much from each other, then you can treat your supply as two single-phase supplies. In that case, I’d suggest an emonPi to measure one phase and run emonCMS, and an emonTx to measure the second phase and send the data to the emonPi. If you do that, you need 2 × a.c. adapter, 2 × c.t, 1 × Raspberry Pi 5 V d.c. power supply, 1 × emonTx, 1 × emonPi, emonCMS.
Which of those two schemes you choose might depend of exactly what you want to measure in total, and what you foresee you might want to measure in the future. The emonTx has four current inputs, the emonPi has two. If you want to measure more than the total house consumption, then all the other things you want to add will affect your decision.