Absolute nonsense. Healthy eating, exercise etc all act to improve your immune system.
Things to take into account why one person gets sick and another doesnt include:
1) basic constitution. Some people are born with a strong constitution and it takes a lot to knock them out
2) sleep. Sleep is one of the best healers. If your DH is getting more sleep than you then he is less likely to get sick. That has to be good quality sleep too
3) stress. Number one killer of your immune system. Increases with sleep deprivation. Mental health plays a part too
4) the definition of "healthy" is often wrong. Low-fat, low-sugar is not necessarily good for you. Good fats including butter are healthy and depriving the body of these essential nutrients can lower the immune system
5) pregnancy & breast-feeding takes an enormous about of essential nutrients from a woman's body and it takes a while to rebuild the stores. Whilst BF can be protective, the nutrient drain can deplete you. When they say a pregnant woman needs to eat for two, it means consume the nutrients for 2 not the volume. That keeps going whilst nursing
6) underlying issues can affect health. Gut health is something I'm learning about, as the effect of gut flora on overall health is extraordinary, from dental health to feet ailments

Keep your fluids up, eat lots of meat soups, preferably made from bone stock, get some early nights, have baths with epson salts and take a probiotic. These will all help boost your system while it's fighting infection.