In what order should I read the Companion Series Vampire novels?

The Companion Series can be read in any order. Each one stands alone. If you haven't read one yet, I would recommend that you read them in the order I wrote them, even though one (THE HUNGER) is a prequel to THE COMPANION.

In that case, the order would be:

SACRAMENT was written several years before the others, and while it occupies the same world, can be read at any time.

Here’s a brief description of how they relate to each other through the relationship of the characters:

THE COMPANION (1818) follows Ian Rufford and Beth. Asharti is the villainess. Ian is helped by first by Colonel Vernon Ware a human and then by Beatrix a very old vampire. Beth's friend is Emma Fairfax.
THE HUNGER (1811) is the story of Beatrix before she meets Ian Rufford, her history with Asharti and her love for John. We are introduced to Stephan Sincai, who mentored both Beatrix and Asharti.
THE BURNING (1820) is the story of Stephan Sincai and Ann Van Helsing. The rogue vampire Stephan is pursuing is Callan Kilkenny, a Scottish vampire.
ONE WITH THE NIGHT (1821) is Callan's story, with Jane Blundell. The villainess is Elyta Zaroff, a friend and mentor to Asharti.
ONE WITH THE SHADOWS (1821) follows Gian Urbano and Kate Sheridan as they struggle with Elyta. Gian's mother, Contessa Donatella Margherita di Poliziano takes them in and helps them.
ONE WITH THE DARKNESS (1821) is the Contessa's story.
SACRAMENT (1818) is the story of Julian Davinoff and Sarah Ashton. One of the villains is Magda Ravel, an old lover of Julian's.

I should mention the novellas:

SACRILEGE is the story, in modern day, of what happened to Magda after she returned to Mirso Monastery.
THE GIFT is the story of Major Vernon Ware and Emma Fairfax and the vampire wars following Asharti's downfall.

I hope this helps you enjoy the stories……