Wiring multifunction fixture to 2 switches, 2-wire cables
Color-coding.  It is your friend. You'll need some black, red and blue electrical tape.  


Go into the switch box.  Confirm that, in fact, the white and black from cable 1 are across switch 1...  And the white and black from cable 2 are across switch 2...   (that is to say, they are not criss-crossed).  If they are criss-crossed, that is bad, make them square.  
Also in the switch box, tape both of the white wires black -- by which I mean wrap several wraps of tape around the wire an inch or two back from the ends.  
Up in the fan box:   Note the two cables coming up from the switch.  Tape both of the white wires black.   We are re-designating these white wires to be "always-hot". ** 
Note the two black wires coming from the switch (partners to the whites you just taped).  Tape one of those black wires red.    
Tape the other black wire blue. This is also a switched-hot.  
Note the third cable coming from supply.  It has a black wire.  Nut it together with the two whites now taped black. 
Now look at the wires which remain loose.  You see a white wire (neutral, from supply), a "red" wire (switched hot from switch), and a "blue" wire (switched hot from other switch).  Also a black bundle pushed back into the box. These are exactly the same wires you'd have on a /4 cable. 
Wire it per factory instructions. 
If the fan needs "always-hot" for some reason, tap it off the black/"black"/"black" bundle you pushed into the back of the box in step 3.  It looks like for the humidity sensor to work, the black wire must be connected to power.  The blue wire is an override telling it to run full speed regardless of humidity. 


If you are not happy with which switch is the fan and which the light, switch them up top.  Do not switch hots at the switch, that would create the crisscross situation we labored to avoid in step 1.  



** When you are forced to use a white wire as "hot", like in a switch loop, there's an advantage to using the white as the always-hot wire.  It's far easier to detect with a voltage tester since it's always-hot.  If it was used for switched-hot, a person might mistake it for a neutral since it is not energized with the switch off.  White wires reused as hots MUST be taped.