Lifetimes of excited states of the nucleus 96Zr were studied with the Doppler-shift attenuation method following the 94Zr(18O,16O)96Zr two-neutron transfer reaction. The obtained B(E2; 2+2 -> 0+2) and B(E2; 4+1 -> 2+2) transition strengths, amounting to 26(2) and 39(7) W.u., respectively, firmly attribute the 2+2 and 4+1 states to the collective intruder band built on top of the 0+2 state. The nature of this structure is discussed against predictions of the collective model using the Bohr Hamiltonian, the interacting boson model with configuration mixing, and the quasiparticle vacua shell model. The collective, interband B(E2; 4+1 -> 2+1) = 11.2(8) W.u. transition strength, refuting the previously assumed purity of both structures, is reproduced in the calculations. The quasiparticle vacua shell model predicts, in agreement with a simple two-state model based on experimental E2 transition strengths, considerable mixing between the normal and intruder 2+ states.