From Rabbi Karo's having written this line, it would seem that he would say that people sleep on their backs. However, he also wrote in his Shulhan Arukh (EH 23.3) thatנותנין המת על גביו ופניו למעלה כאדם שהוא ישןWe place the corpse on its back and its face upwards, like a person when they are sleeping.
Although one could say that, with the latter text, Rabbi Karo means to say that it's kind of like one is lying on one's back, but with the modification of tilting, nevertheless, the first text is still rather interesting. I hope to continue further posts on the topic of Jewish sleep positioning, but, for now, I will end off with the following from Professor Jeffrey Woolf's recent article (HT), thatאסור לאדם לישן על ערפו ופניו למעלה עד שיטה מעט כדי שלא לבא לידי קישויIt is forbidden for a person to sleep on one's neck and one's face turned upwards until one tilts a little in order so that one does not come to have an erection.
When it comes to sexuality, the Shulhan Arukh presents a markedly conflicted stance. On the one hand, the author dutifully codifies the relevant rulings that express a positive attitude toward sexuality. On the other hand, in a section of the work (Hilkhot Zeni'ut) that was more likely to achieve wider provenance (Orah Hayyim), he presents the student with a much more severe, ascetic view of sexuality.- Jeffrey R. Woolf, "'La'avodat Bor'o': The Body in the Shulhan Arukh of R. Joseph Caro," in The Jewish Body: Corporeality, Society, and Identity in the Renaissance and the Early Modern Period, eds. Giuseppe Veltri & Maria Diemling (Leiden: EJ Brill, 2008), 177.