The problem is simple. You can't use the known equations for first order LP and HP for the combined circuit. The load impedance of the second one changes the transfer characteristic of the first. But it's just elementary AC network calculation.
For the general solution, it's comfortable to refer to a symbolic calculation tool, e.g. Sapwin or xfunc. They have been discussed in various same topic threads.
For the first circuit from post #1 (HP/LP) you e.g. get
H(s) = R1C1s/(1 + (R1C1+R2C2+R1C2)s + R1R2C1C2s^2)
The second circuit (LP/HP) only differs by the denominator
H(s) = R2C2s/(1 + (R1C1+R2C2+R1C2)s + R1R2C1C2s^2)
If you are switching from one to the other topogy, also exchanging the R and C values, the term R1C2 makes the difference.