Concerning Heaven:
The Qur’an refers to Heaven as ‘al-janna’, meaning ‘the garden’. It is the home of the righteous; the home of Peace.
Professor M.A.S. Abdel Haleem writes of al-janna:
‘In these pleasing surroundings stand ‘good, peaceful homes’ (9:72) with ‘lofty dwellings built for them, one above the other, graced with flowing streams’ (39:20). There are detailed descriptions of these goodly dwellings (e.g. 55:52–72; 56:15–34; and 88:13–16) – raised couches upholstered in brocade, goblets placed ready, cushions arranged and carpets outspread. We see the dwellers in pleasant company: ‘they will enter perpetual gardens, along with their righteous ancestors, spouses, and descendants’ (13:23; and 52:20–1) adorned in green silk. They sit on couches in a relaxed manner, engaged in pleasant conversation, recalling happy memories, absorbed in rejoicing; their faces shining, laughing and joyous (80:38–9).
‘There is no overt mention in the Qur’an of sex taking place between spouses in janna, although the relationship is lawful between spouses and the Qur’an does not shy away from mentioning it in the context of this world. The mutual love (‘uruban) between spouses in the garden (56:37–8) epitomises the most fulfilling aspect of the relationship between spouses as expressed in the Qur’an: Another of His signs is that He created spouses from among yourselves for you to live with in tranquillity: He ordained love and kindness between you (30:21).’
‘Part of God’s blessing on the righteous is that they will be joined in paradise with the righteous of their parents, spouses (azwāj) and offspring (13:23)…… Al-Janna is not the home of ‘believing men’ only but also of ‘believing women’. (‘Understanding the Qur’an – Themes and Style’; my emphasis).
Concerning the ḥūr:
Allāh (subḥānahu ūta’āla) says: ‘Those mindful of Allāh will be in a safe place amid Gardens and springs, clothed in silk and fine brocade, facing one another: and We shall marry them to fair ones having beautiful eyes.’ (Al-Dukhan: 52-54).
The text ‘We shall marry them to fair ones having beautiful eyes’ renders: ‘wazawwajnāhum biḥūrin ʿīnin.’
We find the same assurance in sūrah ‘Al-Tur: 20’: ‘And We shall marry them to fair ones having beautiful eyes’ (‘wazawwajnāhum biḥūrin ʿīnin’).
Biḥūrin comes from ‘ḥūri’; and applies to both sexes.
In short, men will marry fair companions who are female; and women will marry fair companions who are male.