Lord Shiva and Goddess Kali are husband-wife. Kali is non-different from Parvati.

Infact Kali is Parvati's birth name, given to her by her father Himachala due to her complexion as referenced in chapter 7 of the Parvati Khanda in Shiva Purana:

गतस्तत्र गिरिः प्रीत्या सपुरोहितसद्विजः। ददर्श तनयां तां तु शोभमानां सुवाससा।।६।।

The mountain king accompanied with the priest as well as the Brahmanas went to see the girl who was self illumining.

नीलोत्पलदलश्यामा सुद्युर्ति सुमनोरमाम्। दृष्ट्रा च तादृशीं कन्यां मुमोदातिगिरीश्वरः।।॥७॥

She had the reflection of the blue lotus flowers, looking quite charming with beautiful complexion. The mountain king was immensely pleased by looking at her.

अथो शुभमुहूर्तेऽस्मिन् हिमवान्मुनिभिः सह। नामाकरोत्सुतायास्तु कालीत्यादि सुखप्रदम्॥११॥

Thereafter in the auspicious time, Himacala, in the company of the sages, gave the daughter the pleasant name of Kali.

Chapter 84 of the Devi-Mahatmya recounts how Kali emerges from the body of Durga/Ambika (A manifestation of Parvati)

Thereat Ambika uttered her wrath aloud against those foes, and her countenance then grew dark as ink in her wrath. Out from the surface of her forehead. which was rugged with frowns, issued suddenly Kali of the terrible countenance, armed with a sword and noose, bearing a many-coloured skull-topped staff decorated with a garland of skulls, clad in a tiger’s skin, very appalling because of her emaciated flesh, exceedingly wide of mouth lolling out her tongue terribly, having deep-sunk reddish eyes, and filling the regions of the sky with her roars. She fell upon the great Asuras impetuously, dealing slaughter among the host, and devoured that army of the gods’ foes

In Chapter 6 of the Fourth Book of Devi Bhagavatam, Adi-shakti assigns a consort to Brahma Vishnu and Shiva. This is what she says in Lord Shiva's case:

Brahmâ said :-- Saying thus to Vâsudeva, that Higher Prakriti Devî who is all of the three Gunas and yet transcending them, began to address Mahâ Deva, the Deva of the Devas, in sweet words, thus :-- O Sankara! Accept this beautiful Mahâ Kâlî Gaurî, build a new Kailàsa city and live there happily. Your primary Gunas will be Tamas; Sattva and Rajas will be your secondary Gunas. Have recourse to Rajo and Tamo Gunas while you slay the Asuras and thus wander.

O sinless S’ankara! Have recourse to peaceful Satto Guna, when you reflect on the Supreme Self and practise austerities. You all are for creating, preserving and destroying the Universe and you are all of the three Gunas. There is no such thing in this world as are devoid of these three Gunas.

Lord Shiva and Goddess Kali are husband-wife. Kali is non-different from Parvati.

Infact Kali is Parvati's birth name, given to her by her father Himachala due to her complexion as referenced in chapter 7 of the Parvati Khanda in Shiva Purana:

गतस्तत्र गिरिः प्रीत्या सपुरोहितसद्विजः। ददर्श तनयां तां तु शोभमानां सुवाससा।।६।।

The mountain king accompanied with the priest as well as the Brahmanas went to see the girl who was self illumining.

नीलोत्पलदलश्यामा सुद्युर्ति सुमनोरमाम्। दृष्ट्रा च तादृशीं कन्यां मुमोदातिगिरीश्वरः।।॥७॥

She had the reflection of the blue lotus flowers, looking quite charming with beautiful complexion. The mountain king was immensely pleased by looking at her.

अथो शुभमुहूर्तेऽस्मिन् हिमवान्मुनिभिः सह। नामाकरोत्सुतायास्तु कालीत्यादि सुखप्रदम्॥११॥

Thereafter in the auspicious time, Himacala, in the company of the sages, gave the daughter the pleasant name of Kali.

Chapter 84 of the Devi-Mahatmya recounts how Kali emerges from the body of Durga/Ambika (A manifestation of Parvati)

Thereat Ambika uttered her wrath aloud against those foes, and her countenance then grew dark as ink in her wrath. Out from the surface of her forehead. which was rugged with frowns, issued suddenly Kali of the terrible countenance, armed with a sword and noose, bearing a many-coloured skull-topped staff decorated with a garland of skulls, clad in a tiger’s skin, very appalling because of her emaciated flesh, exceedingly wide of mouth lolling out her tongue terribly, having deep-sunk reddish eyes, and filling the regions of the sky with her roars. She fell upon the great Asuras impetuously, dealing slaughter among the host, and devoured that army of the gods’ foes

In Chapter 6 of the Fourth Book of Devi Bhagavatam, Adi-shakti assigns a consort to Brahma Vishnu and Shiva. This is what she says in Lord Shiva's case:

Brahmâ said :-- Saying thus to Vâsudeva, that Higher Prakriti Devî who is all of the three Gunas and yet transcending them, began to address Mahâ Deva, the Deva of the Devas, in sweet words, thus :-- O Sankara! Accept this beautiful Mahâ Kâlî Gaurî, build a new Kailàsa city and live there happily. Your primary Gunas will be Tamas; Sattva and Rajas will be your secondary Gunas. Have recourse to Rajo and Tamo Gunas while you slay the Asuras and thus wander.

O sinless S’ankara! Have recourse to peaceful Satto Guna, when you reflect on the Supreme Self and practise austerities. You all are for creating, preserving and destroying the Universe and you are all of the three Gunas. There is no such thing in this world as are devoid of these three Gunas.