Gaaaah. I'm such a newbie! Yes, it has that top bar, which used to be no big deal, but now it feels like a big deal. Ah. Specialized. Ooops.
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"What you are referring to as a "men's bike" is a traditional road bike? If so, this is what women ride, too, in many cases. If it fits the way you want it to fit, it won't matter if it has a horizontal top tube. You might even enjoy a touring bike. They're forgiving, they have low gears, and you can put on racks to carry stuff if you want to run errands with it.
BTW, it's 'Specialized.' "