Using a jigsaw to cut both at the same time is
not a good idea.
Too much chance of the blade bending/flexing and you end up with edges that aren't perpindicular to the surface and pieces that are
slightly different sizes.

Which of the following tools do you already own, can borrow from a friend, or are willing to buy?
Circular saw - Used for the long straight cuts.
Jigsaw - Used to make the curved cuts that go from one circular saw straight cut to another and to trim close to the outline of the first side (before finishing it with the router) when making the second side.
Router (pref. full-size, not an el-cheapo laminate trim model) - Used to square up the edges on the first side (especially the jigsaw cuts) and finish the second side with a flush trim bit.
Scott