Generally, when modelling with the intention to use subdivisions later, it's advisable to stick to quads as much as possible, as @brasshat has suggested, since quads produce predictable subdivisions, whereas tris, as you have experienced do not.

In your instance, it's quite easy omit tris. If you have two loop cuts close to one another in the center and then remove the intended faces. For further control you can play with edge crease settings.

Initial quad mesh

Removing the desired faces

Subdivided mesh

(FYI, As @David has mentioned, any comments related to a specific answer should go as a comment below the answer which you would like to discuss. This makes it easier to build an accurate reference catalogue of questions and answers that others can reference later)

Generally, when modelling with the intention to use subdivisions later, it's advisable to stick to quads as much as possible, as @brasshat has suggested, since quads produce predictable subdivisions, whereas tris, as you have experienced do not.

In your instance, it's a bit difficult to decipher what your intended result is. 

If you would like to remove some faces, you could have an extra loop cut. If you have two loop cuts close to one another in the center and then remove the intended faces. For further control you can play with edge crease settings.

Initial quad mesh

Removing the desired faces

Subdivided mesh

If you would like to create a sharp edge, you could play with the edge crease settings, and creating loop cuts that are very close together.

Quad mesh with extra loops cuts and crease settings changed

(FYI, As @David has mentioned, any comments related to a specific answer should go as a comment below the answer which you would like to discuss. This makes it easier to build an accurate reference catalogue of questions and answers that others can reference later)