As stated, it depends on the parts. However, for the most part the answer is yes.
The 96-98 Civics have a completely different Front End than the 99-00 Civics, so if you were to put say a "hood" from a 96 DX into your 99 Si, you couldn't unless you also change out the Fenders, Headlights, Bumper and Grill. The Rear End, as far as body panels, is interchangeable so you can use the trunk lid off any model 96-00 Civic in your 99-00 Civic Si. Same goes for the Tail Lights, Rear Bumper, etc. Have in mind that 96-98 Tail Lights are different than 99-00 Tail Lights in appearance, but not in shape/form so you can interchange them without issues. This also applies to the Rear Bumper (96-98 is different than 99-00 in looks).
The Suspension (Shock/Spring) is interchangeable between 96-00 Civics no matter the model. The Front Lower Controls Arms & Strut Forks off the 99-00 Si is not the same as other model 96-00 Civics though - they are wider and thicker. The Rear Lower Control Arms are the same throughout all the models in the 96-00 Civics. The 99-00 Civic Si, however, is the only 96-00 Civic that has Rear Disc Brakes as all the others have Rear Brake Drums.
The Engine of the 99-00 Civic Si is a B16A2, its the only 96-00 Civic that comes with a DOHC VTEC Engine from factory, the rest come with either a D16Y7 SOHC Non-VTEC (CX, DX, LX) or a D16Y5 or D16Y8 SOHC VTEC (HX, EX) Engine. No engine parts are interchangeable from the D16 to the B16. You could use the SOHC Engine Mounts on your DOHC Motor though, that's about it.
The Interior of the 96-00 Civics are all interchangeable without needing to modify anything, so have fun there. The 99-00 Civic Si comes with all the factory goodies you may want, so I'm not sure what you'd want off a 96 DX.
I'm sure I'm missing a few thing, but this gives you a quick overview of what is interchangeable and what is not. If you could be more specific then we may be able to assist you a lot better in answering your question on whether that part is interchangeable or not.