My parents—more specifically, my mum—doesn't believe in mental illnesses. She calls depression a feeling that'll go away if you just think about being happy and believes that anti-depressants are simply money-making placebos... If I were to tell them about how I feel, they'd deny it. Help?

well Charlie, I don't know about other people but ever since I started thinking about happy things i've been less depressed, but no two people are the same so it might not work for you, how about you do some research and show your mum scientific evidence proving that mental illnesses are a real thing, and then she cant say otherwise because only science can disprove science.

depression is a hard thing to dell with especially with out support .
to help others understand it i herd depression be compared to asthma: with asthma your body is not getting enough air , and with depression your body is not getting enough dopamine (for those who don't know dopamine in the chemical in your brain that helps you be motivated,the "happy" chemical of the brain)
you should do as Krollo said it usually helps parents don't believe its a thing understand. also if your in school/college and you feel up it most usually have counselors who can help.
and about the anti- depressants: when you go to the doctors if you ask for bettor detail but i believe that the meds are ether suppose to help your body make more dopamine and/ or open the receptors for the dopamine to go. it really depends and the doctors will have you come in at least ounce a week for therapy to see how its going, but i think that depends on the hospital.

This^

Check to see if your school has a SAP program. As most of them do. For an instance my school has one where they bring in licensed therapists for each student's needs. They can diagnose you and even write prescriptions.

try seeking therapy or someone to talk to. like a school psyche or consular. Try looking up scientific depression facts and showing her lol. if you feel this way there is no need to be ashamed, you deserve to have someone who believes you.

I'm depressed. And I want you to know that before you read the rest of this message.

Your mother is not completely wrong. Placebos do exist, and they can have the effect of actual medicine. HOWEVER this is NOT the case for depression!

Consider telling your mother this: depression is caused by a chemical imbalance in the brain. Medication puts chemicals in the brain to restore balance. Obviously, medication is not the only solution - therapy helps as well. So does going out with friends. But the order isn't Sick Brain --> Happy Thoughts --> Happy Experiences --> Healthy Brain.
This is what happens: Sick Brain --> Somewhat Fun Experiences --> Okay Thoughts --> Not-As-Sick Brain.

Depression is a chemical imbalance, and medication restores balance. Tell her that, show her pictures, and say this: if happy thoughts cure a depressed brain, then healthy thoughts should cure a cancerous brain, right?