"If DNA is complexed with cationic liposomes, does it stay complexed on the surface or there's some kind of rearrangement of the structure?"
It mainly depends on the molecules surrounding the complex. Interaction between DNA molecules and cationic liposomes is mainly a relatively strong electrostatic interaction. The system should remain as a complex until stronger forces detach / separate the molecules.
A scholar with Chemistry degree / background may provide better explanations.