It depends on what the message is that they are receiving.
I don't think you can when there are two standards in the house. "Do as I say, not as I do" is a really tough model to follow. I think, if it's something like beer, you can easily say, "This is for adults and not for kids who are still growing." But when Dad can have cookies and they cannot, you've got a huge disconnect.
But how and when is Dad eating these products? Are they a small treat now and then after a healthy meal and a trip to the gym? Or is the message, "These are my treats, don't touch them, and I don't give a damn if your mother wants you to eat kale chips, I want my Fritos"? If the parents don't agree on a fundamental issue, the kids pick up on the disconnect, and play one against the other.
However, if the treats are limited and are the high quality version, that's a different story. So, for example, if your husband is eating (or will switch to) a high-cacao dark chocolate and not eat the whole bar, that has a beneficial health effect on the heart. A few chocolate shavings or dark chocolate chips over a dish of frozen yogurt can be really fun.
If the cookies/treats you both buy are higher in whole grains and limited in processing (and with no trans fats or high fructose corn syrup), or better yet if you make them yourself with natural sugars (stevia, agave), oats, whole grain flour, etc., that's another story. So see if you can make some "acceptable" switches for everyone that put healthier choices in front of them.
My son is a hard core runner who watches everything that goes into his mouth (having evolved from the pickiest eater of chicken nuggets, fries and junk if I'd let him), but he likes these granola bars made with almond butter or peanut butter (he uses the natural, with no high fructose corn syrup), dried fruit (cranberries, currants, dried cherries, etc. - we mix it up), oats, and so on - and no preservatives. Far better than packaged granola bars that the industry tries to make you think are healthy! Getting the whole family involved in some shopping and cooking is fun, and it rubs off. Even limiting an ingredient list to something like 5 or 6 ingredients, or saying that the first 5 can't contain "sugar" or "partially hydrogenated oils" or "enriched flour" is a huge step in the right direction.
Another reason people snack is that they are craving nutrients they are missing. It's been well documented for decades that our food supply is deficient because of over-processing, depleted soils, and unhealthy growing techniques. So our bodies are missing things, we crave those phytonutrients or trace elements, and we head to the cabinet to grab whatever is there. Upgrading the nutrient load of what you eat for regular meals is a good start, and supplementing properly with bioavailable (absorbable) nutrients with a patent on the label (so you know that what is says on the label is actually in the can!) is a great step. We found it cuts the cravings because we are fully satisfied and our nutrition needs are met, so the treats are just that - a treat. Two cookies will do instead of 10, an ounce of chips with a healthy dip just taste so much better than a half a big bag, real chocolate tastes so much better than a bar of cheap chocolate with HFCS, and so on. When kids' palates are expanded and updated, they make better choices naturally, so Mom isn't the Food Police Chief.