both horizontal and vertical subequations

Question

I've been having a really hard time figuring out how to accomplish a both vertical and horizontal subequation block while they are still aligned, so that it would look something like:

(1a,b) ...=...=..

(1c) ......=......

(1d) .....=......

I usually use subequations with align environments to produce aligned vertical subequtions and the following code to get the mix but if i have a big set of subequation and i need them aligned it doesn't work. Help pls..

\refstepcounter{equation}
$$
\label{initial_rey}
h(t=0)=h_0,
\eqno{(\theequation{\mbox{a}})}$$
$$
\frac{\partial p}{\partial x}\bigg|_{(x=0,t)}=0, \quad \mbox{and} \quad
p(x=L,t)=p_e,
\eqno{(\theequation{\mbox{b},\mbox{c}})}
$$