What you are asking is possible in OpenGL 3.2. I've got my FBO spitting out diffuse colour to a colour texture, normals to another colour texture, and depth to a depth texture -- no renderbuffers needed. In fact renderbuffers are just a problem, because you cannot sample from them, so you'd have to use
glReadPixels(...) or otherwise somehow copy the data out of the RBO and into a texture on the CPU, instead of just maintaining everything in GPU memory. So...
If you really want to, you can write code in your first-pass shader to manually output stuff like depth, to a separate colour texture attachment in your FBO. That would be for use by you in your post-pass shaders. For OpenGL's use in its internal depth-testing, you would additionally need either an RBO or texture set as your FBO's GL_DEPTH_ATTACHMENT. But you can set up a single texture to serve both -- this is more efficient & easier to use.
My depth texture setup code looks like this (Java, just ignore the ByteBuffer stuff... and note I use "id" to refer to integer handles/pointers, since that concept doesn't really sit well in Java):
gBufferDepthTexture = new Texture();
gBufferDepthTexture.id = glGenTextures();
gBufferDepthTexture.unit = 2;
gBufferDepthTexture.width = Display.getWidth();
gBufferDepthTexture.height = Display.getHeight();
gBufferDepthTexture.bytes = ByteBuffer.allocateDirect(Display.getWidth()*Display.getHeight() * 4);
glActiveTexture(gBufferDepthTexture.unit + GL_TEXTURE0); //eg. 0 + 33984 = GL_TEXTURE0, while 31 + 33984 = GL_TEXTURE31.
glTexImage2D(GL_TEXTURE_2D, 0, GL_DEPTH_COMPONENT, gBufferDepthTexture.width, gBufferDepthTexture.height, 0, GL_DEPTH_COMPONENT, GL_FLOAT, gBufferDepthTexture.bytes);
//...GL_UNSIGNED_INT or GL_UNSIGNED_BYTE may work better for you, instead... YMMV.
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_S, GL_CLAMP);
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_T, GL_CLAMP);
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MAG_FILTER, GL_LINEAR);
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, GL_LINEAR);
//your existing glFramebufferTexture2D(...) calls here
glFramebufferTexture2D(GL_FRAMEBUFFER, GL_DEPTH_ATTACHMENT, GL_TEXTURE_2D, gBufferDepthTexture.id, 0);
You can now pass
gBufferDepthTexture (or what have you) as a uniform to your second, third pass fragment shaders. I think we can safely assume that you can do exactly the same thing with the stencil buffer.