Ask Mr. Smarty Plants

You are not alone in your frustration with aphids, whiteflies and spider mites. These are the most troublesome pests of indoor and greenhouse plants. Just be thankful you don’t have mealybugs and scale to contend with - which are worse pests.
The pests that are attacking your herbs, perennials and shrubs are a prevalent problem because they have very short life cycles and can multiply exponentially very quickly becoming a devastating crisis almost overnight. Aphids can bear live young and have those offspring produce their own babies in as little as seven days under ideal conditions.
Aphids, whiteflies and spider mites also all have a very large list of host plants that they like to attack. When they do this they feed on the plant sap of your plants. Large infestations will decrease the vigor of the plant, may distort new growth (particularly aphids) and could ultimately kill the plant. The challenge in controlling these pests is that because their life cycle is so short there are lots of young appearing and any control will have to be repeated several times and in short intervals.
Biological controls such as ladybugs, lacewings, and numerous targetted predatory insects have been very successful in many greenhouses where there is a closed environment. In this situation the biologicals can be monitored, released at strategic times, and kept in the area where they can do the most good. Ladybugs released into a yard will most often fly away searching for their own food and not attack the pests that gardeners want them to attack. Ladybugs are freewheeling and are beneficial to all the neighborhood and less so for a specific area.

Here are some pest control strategies to consider:

• Prune back plants – this will make them easier to spray and removes some of the pest eggs.
• Spray the undersides of the leaves – this is where most of the pests are located.
• Inspect your plants every 2-3 days. Get a hand lens to see spider mites on the underside of leaves.
• Keep plants from being stressed. Stressed plants are more prone to attack by pests. Avoid extremes of watering (excessively wet or dry). Fertilize regularly during the growing season. Repot plants regularly, and give them adequate sunlight and air movement.
• Spray incoming plants with an insecticidal soap (as long as this won’t harm the plant) as a preventative measure - even if they look clean. Quarantine new plants for at least 2 weeks if they are suspected of carrying pests.
• Use yellow sticky cards near whitefly prone plants to monitor the pest.

There are a lot of resources online about managing these pests in a greenhouse (which is close to your situation). Some examples include:

Greenhouse Insect Management

Managing Aphids in the Greenhouse

Greenhouse whitefly