Ace novel (?) - alternate universe hopping couple

Question

I read this book in the early '80s. Based on cover art/style, the book was published in the late 60's/early 70's. Pretty sure it was an Ace novel, possibly a double novel. The cover featured a man running from what is presumably the antagonist of the story, which might have been a giant head (I might be conflating this with another book I read at the time). I believe he was with a woman, they might have been holding hands. The background was black, with abstract but multicolored linear details.

In it, a man is on the run from some evil and can somehow escape through alternate realities. On his way, he encounters a girl whom he takes with across realities. The only other salient detail I remember is that, when they arrive at one world, they are in a forest, and make breakfast from eggs found in a nest by cooking them on a hot stone in some way. Recall nothing else of the story.

Answer 1

This is a long shot, but could it be The Chalice by Deborah Chester. This is the third book of her The Sword, the Ring and the Chalice series:

At their backs, the sun was coming up, streaking the sky with coral and gold. With it came the heat that was their enemy. Dain frowned at Alexeika, who was making odd little noises in her throat.

“What?” he asked again.

“Eggs,” she said reverently. “A nest of eggs.”

Nearly overwhelmed by this stroke of good luck, he closed his eyes. “Merciful Thod,” he whispered.

“Can you reach them?”

“Aye. Here.”

With infinite care, she handed the fist-sized eggs down to him one at a time. He fought off the darsteed, which lunged at their bounty, and managed to keep the beast from stealing any. Grumbling, the darsteed lurched off, then stopped, glaring back at them with red, resentful eyes.

Ignoring it, Dain and Alexeika busied themselves making camp a short distance away from the water hole. Alexeika built a fire, while Dain held up the eggs one by one. They were hard-shelled and an ugly greenish-black color. Four of them felt heavy; two did not.

He and Alexeika baked the four heavy eggs in the ashes of the small fire, their mouths watering at the aroma. The darsteed stayed nearby, bugling its desire for food. Finally Dain tossed it the lightweight eggs he’d rejected. Two snaps of the darsteed’s jaws, and the eggs were gone. Go, Dain commanded, and finally the darsteed ambled off to hunt.

When the eggs were cooked, Alexeika rolled them out of the ashes with a stick. They cracked one carefully on a stone, not sure what they would find inside. But there was a yolk, bright orange and steaming, in the midst of flaky white.

Sniffing it cautiously, Dain smelled nothing foul. At his nod, Alexeika divided the egg between them, and they could barely wait for it to cool. Dain found the flavor too strong to have been appealing under different circumstances, but he ate all of his share and counted himself blessed.

The story seems only tenuously related to your description, though the protangonist Dain does move through different worlds searching for the eponymous chalice. However it was published by Ace as you remember.

Answer 2

Possibly Murray Leinster's Gateway to Elsewhere, published in 1954 in Ace Double D-53 (with A. E. Van Vogts's The Weapon Shops of Isher).

The cover has a giant head and a man with a woman:

and from the inside-cover blurb:

”There are other worlds… and it is possible to travel from one to another. In fact, we constantly visit the frontier cities without ever knowing it!”
Tony Gregg was just an ordinary everyday American until the day he came into possession of an old Barkut coin. He knew it was more than just a collector’s curio because there was no such place on any map of Earth, past or present. He learned then that it could be used as a key — a key to a GATEWAY TO ELSEWHERE.
That was the beginning of one of the most fabulous and fantastic adventures that ever befell a young man looking for excitement. For Gregg plunged forthwith into a fourth-dimensional world of the Arabian Nights, where the djinns of Aladdin’s Lamp were rampaging realities, and a lovely princess was waiting to be rescued!

So it has interdimensional travel, at least between two universes, maybe more from the sounds of it.