There is an optional rule in the DMG (p. 266-267) for Healing Surges:
As an action, a character can use a healing surge and spend up to half his or her Hit Dice. For each Hit Die spent in this way, the player rolls the die and adds the character's Constitution modifier. The character regains hit points equal to the total. The player can decide to spend an additional Hit Die after each roll.
A character who uses a healing surge can't do so again until he or she finishes a short or long rest.
Under this optional rule, a character regains all spent Hit Dice at the end of a long rest. With a short rest, a character regains Hit Dice equal to his or her level divided by four (minimum of one die).
The rules for a Short Rest (PHB p. 186) state:
A character can spend one or more Hit Dice at the end of a short rest, up to the character's maximum number of Hit Dice, which is equal to the character's level.
This leads me to two questions about how these things interact:
1) If a character has spent Hit Dice on a Healing Surge, can he or she still spend additional Hit Dice at the end of a Short Rest? (I think yes.)
2) What is the order of things happening "at the end of a short rest" — does the character regain level/4 HD first, and then might re-expend those immediately, or does he expend as many as he or she wants and has left first, and then regains level/4?
Best Answer
Before all considerations, you've got to ask yourself what is this particular optional rule trying to achieve.
In the text block preceding the one you quoted, you can find that goal:
By adding Healing Surges in combat, the DM aims to make hit points easier to regain between long rests.
Thus, allowing the expense of hit dice both in combats and short rests seems to concur to that goal.
As for the order in which things occur at the end of a short rest, it's up to the DM's decision (see it as fine tuning the difficuly of the game). Having the players use any hit dice left before regaining 1/4 of their maximum number will ensure they will have at least one to spend on the next encounter. On the other hand, allowing the 1/4 recovery before any short rest expense of hit dice will lead to healthier PCs at the start of the next fight.
tl;dr : Yes, you can use both. On short rests, the DM decides if you regain some hit dice before you expend any, or the other way around.