Toast the allspice, cinnamon, nutmeg and a pinch of salt in a medium saucepan over a medium heat until fragrant, about 2 minutes. Add the chicken stock and bring to a simmer. Place the couscous in a medium bowl. Pour the seasoned stock over the couscous and add the raisins. Gently stir to combine, then cover with plastic wrap and allow to sit until the stock is absorbed and the couscous is fluffy, 10 to 15 minutes.
Meanwhile, heat the olive oil in a large saute pan over a medium heat and cook the onions until translucent, stirring often, about 8 minutes. Add the garlic and cook for 2 more minutes. Season with salt and pepper.
Add the mushrooms and cook until softened and caramelized, 5 minutes. Add the Swiss chard and continue to cook until it is fully wilted, 3 to 5 minutes. Taste and adjust the seasoning as needed.
Toss the Swiss chard mixture into the couscous along with about half of the parsley, then stir. Top with the remaining parsley and serve warm.