I don't think LabVIEW DAQ hardware supports triggering on both edges. It appears you have to trigger on one or the other.
The only thing that I can think of to try is to take your analog signal and split it into two different analog inputs. Use the example "Acq&Graph Voltage-Int Clk-Dig Start.vi". Insert it in a new vi twice. You will have to open it and modify the connector so the Physical Channel and Trigger Edge are inputs and the graph is the output. Then wire each one with a different analog input and trigger edge and run them sequentially. Hopefully it will run fast enough for you.
Randall Pursley