Combine beer, lemon juice, mustard, garlic, herbs, spices, and salt in a medium bowl. Slowly whisk in oil. Taste for seasonings and adjust accordingly.
Trim off excess skin (just the straggling bits) on chicken thighs and drumsticks. Place into a deep plastic or glass bowl (large enough to fit all of the chicken), and pour marinade over top. Using tongs, gently toss to coat. Cover bowl tightly with plastic wrap and place into the refrigerator for 4-6 hours.
Prepare your grill for indirect cooking.
Remove chicken from the marinade, and place them onto the cooler part of the grill. Reserve the marinade and brush onto the chicken during the first 2-3 minutes of grill time. Do not apply marinade after that.
Close the lid and let the chicken cook for 45 minutes, or until the internal temperature reaches between 165-170 degrees F. Move chicken over direct heat (hot) and sear for 2-3 minutes per side to form a nice crust.
Once cooked through, remove chicken from the grill and place onto a clean serving platter. Serve with your favorite sides.